Why did the Eastern Roman Empire Survive?
The last emperor of the united Roman Empire died in AD 395. Thereafter, the two halves went in very different directions. Looking at a map of the Mediterranean in AD 400, it's hard to imagine that within 76 years, the Western Roman Empire would vanish while the Eastern Roman Empire prospered. How could they experience such different fates? I will argue that two relatively simple things account for much of this divergence in destinies: a) circumstantially favorable geography and b) Constantinople, the cosmopolitan and formidably-defended capital of the Eastern Roman Empire. I'll look at why these two advantages worked in tandem to save the Roman east from destruction while the Western Empire's vulnerability ultimately doomed it.
First, probably the most critical factor in the Eastern Roman Empire's survival in the fifth century was the fortune of geography. Historian Bryan Ward-Perkins sums up this widely held view:
"The decisive factor that weighed in favor of the East was not the greater power of its armies and their consequent greater success in battle, but a single chance of geography - a thin band of sea (the Bosphorus, Sea of Marmara, and Dardanelles), in places less than 700 meters wide, that separates Asia from Europe." 
But that "thin band of sea" was enough to protect the eastern provinces of the Empire. Most invaders had no way of crossing into Asia, especially with the Roman navy guarding the crossing points.
Instead, they chose to stick with the easier prey found in the Balkans. The Eastern Romans knew how vital this water barrier was to their safety, publishing a law in AD 419 that made it a capital offense to teach the barbarians the skill of building ships. 
Beyond the Hellespont, the geography of the eastern provinces helped in other ways as well.
Egypt was safely nestled in the southeastern corner of the Mediterranean; it was surrounded by vast deserts on both sides and protected by its distance from the instability enveloping the Empire's European holdings. Likewise, with its populous coastal cities and bustling trade networks, Anatolia was surrounded on three sides by water, making it safe from the threats the Western Empire was facing. In the Levant (roughly Syria and Palestine), difficult terrain and a chain of massive border fortifications secured the Empire's eastern flank. Now and then, invaders would make it through. For example, the Huns briefly came out of the Caucasus in AD 395 to threaten Antioch. Generally speaking, however, the eastern frontier did not experience the level of instability that the Western Empire did.
Persia remained a dangerous foe and constant threat, true, but the century after the death of Theodosius I (AD 395) saw an almost uninterrupted century of peace between the two superstates. This last point is crucial because it's an important caveat to my argument that geographic circumstances saved the Eastern Romans.
Some of these geographic advantages I'm arguing for were situational ones since the Persian front was quiet. Had the Eastern Romans been forced to fight on two fronts, as they would be again from the sixth century on, things may have gone differently. For example, the early seventh century's cataclysmic Roman-Persian war would see the Persians make deep advances into Anatolia, the Levant, and even Egypt.
Again, I want to emphasize that these geographic advantages were not permanent fixtures, but temporary ones specific to the fifth-century geopolitical situation. In later centuries, the Romans' most dangerous foes would push from the east. First, Persia, when it resumed hostilities in the early sixth century, and then the even more dangerous Arabs and Turks after that.
Meanwhile, pressure in the European theater would continue unabated, with Goths and Huns eventually giving way in later centuries to Avars and Bulgars. However, during this period, from AD 400-500, the Eastern Roman Empire's primary threat came from Europe's barbarian migrations. In this respect, at least, they were fortunate to face only this one dangerous front.
Constantinople - The Perfectly Placed Capital
Thanks to Roman ingenuity, not all of these geographic advantages were transient. One in particular proved crucial to the Eastern Roman Empire's long-term survival. This was the establishment of Constantinople by the Roman emperor Constantine (AD 306-337), who understood the strategic importance of the Bosphorus for ruling his empire.
It was a wise choice offering several advantages.
First, it straddled Asia and Europe, placing it equidistant from the Empire's strategic priorities. The ever-threatened Danube frontier was nearby to the west; the rich cultural urban centers of Anatolia and Syria were easily accessible by sea.
The Empire's breadbasket, Egypt, connected the capital with a steady supply of grain.  In short, the city was strategically well-placed, serving as the gateway between Europe and Asia, and was easy to defend and supply. You could not have asked for a better capital city for an empire beset by enemies.
By AD 430, Constantinople was the most important city in the Empire, with a population of over 250,000.  Located on a triangular-shaped peninsula and surrounded by water on three sides, Roman engineers protected the vulnerable landward side with an integrated system of defenses: first, a moat 20 meters wide and 10 meters deep; behind that, an outer wall 2 meters thick and 8.5 meters high with 96 towers spaced at 55-meter intervals; and, finally, an inner wall 5 meters thick, 12 meters high, and also with 96 towers spaced out at 55-meter intervals. 
The Empire would face much darker days than those experienced in the fifth century, but the capital's defenses would keep enemies at bay until the Fourth Crusade in AD 1204. Flash forward a thousand years to 1453, and the very last bit of territory the Byzantines held was that of their capital. Even then, the Ottomans only overcame those defenses with great difficulty by deploying cannons against the city's ancient walls.
But in Late Antiquity (AD 350-550), Constantinople became a real cosmopolitan capital, a hub for everything. Shipyards built and maintained the navy. Massive granaries fed the population. Workshops within the city manufactured weapons for the army. The capital had everything in one location, and its enemies could do little about it.
Not only was Constantinople the greatest city in the Mediterranean by the later fifth century, but it became the political and intellectual hub as well. Throughout its long history, and in contrast with the Western Roman emperors, Eastern Roman rulers would not feel compelled to transfer the capital to a more advantageous location, at least until forced to do so by Crusaders and Venetians in AD 1204. Nothing else could even remotely compete with Constantinople.
In addition to the Imperial Court, the Patriarch of Constantinople, the imperial bureaucracy, the Navy, the Army, the Senatorial aristocracy, all of these were based in the capital, centralizing power in one place under the emperor's iron grip. Important power centers like these became complementary and force-multiplying by being co-located in the same city. This level of consolidation, combined with the geographic advantages discussed above, helped the Eastern Roman Empire get through the fifth century intact.
Why Geography Mattered
If geography worked in the East's favor, it did not do so uniformly. Think of the Eastern Roman Empire as divided into four distinct geographic zones: Egypt, the Levant, Anatolia (Asia Minor), and the Balkans. Of these, the first three were particularly critical to the Empire's economic health. Outside of the capital, the largest and oldest cities were in Egypt (Alexandria), along the southern Anatolian coastline, Syria (Antioch), and Thrace (Thessalonika), just to name a few.
However, Eastern Roman possessions in the Balkans suffered enormously during the fifth century and can be considered a geographic extension of the Western Empire. What the Western Romans suffered from barbarian incursions, the Eastern Romans suffered as well in the Balkans.
Barbarian war-bands and migrating peoples increasingly roamed at will, plundering and pillaging their way from one end of the Balkans to another. First, the Visigoths did so between AD 376-408, then the Huns in the AD 440s, and finally the Ostrogoths (AD 459-488). Parts of the northern Balkans came to resemble Gaul north of the Alps after AD 406, a dangerous place where the central government's rule was often tenuous, at best.
Facing the same threats in the European theatre, one can go a step further and argue that the Eastern Romans actually performed even worse than their western counterparts. Unfortunately, the Roman military between AD 395-495 was a shambles on both sides of the Empire. The fearsome Roman war machine of legend was by then a faded shadow of its former self.
While Roman arms had remained formidable throughout much of the fourth century, the destruction of Eastern Emperor Valens' mobile field army at Hadrianople in AD 378 by the Visigoths was a devastating blow that took years to recover from.
Edward Gibbon famously summarized the fiasco: "The event of the battle of Hadrianople, so fatal to Valens and to the empire, may be described in a few words: the Roman cavalry fled; the infantry was abandoned, surrounded, and cut to pieces." 
With their emperor dead and his veteran field army destroyed, the Eastern Romans were left to trust in Constantinople's defenses. They were right to do so. The victorious Goths were intimidated by the size of the capital's walls, deciding in the end that they did not have the means to capture the great city.
Ammianus Marcellinus, a contemporary Roman historian of this period, wrote,
"Their [Visigoths] spirit was further damped when they contemplated the long circuit of the walls and the huge extent of the blocks of buildings within them, the beauties of the city beyond their grasp, its vast population, and the strait nearby which separates the Black Sea from the Aegean. After suffering greater losses than they inflicted they dismantled the works that they were constructing, and left the neighborhood to spread themselves over the northern provinces." 
Later, in AD 468, the Eastern Roman emperor Leo I (AD 457-474) teamed up with his Western Roman colleague Anthemius (AD 467-472) to recapture the former Roman province of North Africa, lost to the Vandals several decades before. Like seemingly every major Roman military endeavor of this period, it ended in a fiasco.
The Vandals destroyed the invading fleet, the army disintegrated, and the Western Empire soon breathed its last gasp. Leo had bet big on this expedition and lost big, reportedly committing the entire imperial reserve to the expedition. 
I cite these examples to show that, despite this dismal record of performance on the battlefield, Eastern Roman core holdings managed to survive intact even as the Western Romans crumbled. Again, it's important not to underestimate the relative immunity from invasion that these interior provinces enjoyed thanks to the Bosphorus, Constantinople's walls, and a long peace with Persia.
According to Goldsworthy, "The archaeology suggests that many of the eastern provinces were thriving with high populations and good agricultural productivity. Again, the general freedom from raiding over the course of the century was in marked contrast to the western provinces and doubtless contributed to this prosperity." 
The East's safety meant that the Imperial government in Constantinople always had a reliable tax base. Every defeat on the battlefield, every failed campaign - and there were many of both during this period - could be endured because gold continued flowing into imperial coffers. The government could raise new armies, build better fortifications, and even pay off invaders with gold.
This last option was vital because it gave the Imperial Court another policy tool, money. Gold could achieve what arms could not, at least to a certain point. When dispatching an army was not an option, Eastern Roman emperors had no qualms about buying peace and usually had the cash to do so, even if they knew the peace they were buying was no more than a brief pause.
Yes, this was a classic case of throwing money at a problem, but it offered a viable way out of an otherwise hopeless military situation. While this kind of foreign policy may sound like groveling weakness to modern readers, it was a surprisingly effective means of getting the fifth century Eastern Romans out of unwinnable wars.
Moreover, the gold-hungry invaders were often willing to take the easy money the Eastern Empire offered rather than fighting for it. One can even think of these barbarian incursions as large-scale extortion exercises.
Both sides understood this, and negotiations centered around this dance between barbarian demands and Roman largesse. The Eastern Romans, in contrast to their cash-strapped Western colleagues, could afford to do this dance. They had the money to make their problems go away, if only for a little while. The West increasingly did not.
Take a fairly typical example from the middle of the fifth century when the Eastern Empire's military fortunes reached rock bottom: Attila attacked the Balkans in AD 442-443 and destroyed several Roman cities. A Roman army left Constantinople to confront him and, like most Roman armies of this time, suffered a resounding defeat in AD 443.
The eastern emperor Theodosius II bought peace by agreeing to have the previous annual gold tribute tripled to 2100 Ibs and by offering an immediate one-time payment of 6000 Ibs. This onerous treaty purchased a few years of peace before Attila again decided to shear his Roman sheep in AD 447. 
And so this cycle repeated. Another Roman army was dispatched, and another was promptly destroyed, resulting in another costly peace treaty. And so, the precarious balance was temporarily restored. Though the sums extorted from the Romans were enormous, it's worth noting that they could still pay them without bankrupting the government. Attila eventually went west and died there. The immediate threat passed, and the Eastern Romans survived to bribe another day.
Why the Western Empire Failed
The Western half of the Empire was not so lucky, and after AD 476 disappeared from the historical stage. Lacking the advantages of geography and a cosmopolitan capital like Constantinople, the West's structural disadvantages proved impossible to overcome.
Why is that?
First, unlike in the East, power centers were fragmented. Political power followed the imperial court, which by the early fifth century had settled into the insignificant but defensible city of Ravenna in northern Italy.
Since the late third century, the Western capital had moved with the emperors. These relocations were responding to circumstances. Emperors needed to be near the action, and the action was close to the beleaguered frontiers along the Rhine and Danube. However, over time, distinct disadvantages to this way of governing emerged.
Historian Adrian Goldsworthy summarizes the contrast between the eastern and western capitals quite well:
"There [Ravenna] the western emperors were isolated. The Senate's power had long since become symbolic, but it still consisted of rich and influential men. Both they, and other important figures including the pope, were in Rome, some distance away from ready access. A constant stream of petitioners and people seeking favors from the emperor still flowed to Ravenna, or wherever the capital happened to be, but in no respect was it an especially important city. Constantinople was genuinely the heart of the Eastern Empire." 
These disconnected western emperors holed up in Ravenna stopped leading armies as before and delegated military authority to a series of powerful generals (Stilicho, Constantius III, Flavius Aetius, Count Boniface, Ricimer) who operated elsewhere with personal agendas that often conflicted with those of the emperors they supposedly served.
But what about Rome?
Rome was still the largest city in the Empire, at least in AD 400, but it now existed on the margins of imperial politics. That trend would only accelerate in the fifth century. Emperors no longer ruled from Rome, nor did they even bother to spend much time in the Empire's former capital.
That said, if Rome's importance as a political capital was waning, it was now the seat of the Papacy which, during the fifth century, would begin to step in and fill the power vacuum left by the collapsing Western Empire. Rome would begin its transition from a political center of power to a spiritual one, though the culmination of that role was still some centuries in the future.
Unlike the eastern half of the empire, geography was also not friendly to the western emperors. The Rhine and the upper Danube represented the traditional barriers separating the civilized Romans from Germania, but these were long and remote frontiers to defend.
During times of political stability, the frontier was defensible thanks to the Empire's sophisticated administrative and logistical networks. These ensured the efficient utilization of the Empire's resources spread across its vast span. Normally, lower-quality border troops stationed on the frontiers provided an initial layer of defense near the frontiers until the highly professional mobile field armies could arrive to repel the invaders.
Increasingly, however, the border troops on the frontiers struggled to meet these emerging threats. The mobile field armies that had played such an essential role in maintaining Rome's borders in the third and fourth centuries also struggled to meet all the dangers.
The Romans mostly had themselves to blame.
Several costly civil wars in the late fourth and early fifth centuries (Magnus Maximus vs. Theodosius between AD 383-388; Eugenius vs. Theodosius between AD 392-394; Honorius vs. Constantine III between AD 407-411) siphoned troops from the borders to fight other Romans. Once the dust settled, and a victor emerged in these bloody contests of Romans killing Romans, the frontier defenses never quite returned to the same level as before.
After Hadrianople in AD 378, the Roman armies increasingly relied on barbarian allies to fill out their ranks. For example, in the civil war against Eugenius (AD 392-394), Theodosius relied on a large contingent of Visigoth allies to do the brunt of the fighting on the first day of the battle.
Something had to give, and it finally did. In the summer of AD 406, the Romans had stripped the frontiers bare to scrounge up troops to defend Italy from a major barbarian incursion. The Romans under Stilicho were victorious, but they paid for it later that year.
According to J.B. Bury, "For the Rhine was virtually undefended at the end of AD 406, when hosts of Germans crossed the river and began a progress of destruction through Gaul. This event was decisive for the future history of Western Europe, though the government at Ravenna had little idea what its consequences would be." 
These "hosts of Germans," mainly Vandals, Alans, and Suebi, never again left the Empire, first devastating Gaul before moving on to Spain. The consequences were devastating for the Western Empire. This invasion was no mere raiding expedition as before, but a one-way migration into the Empire's rich but now weakly defended western provinces.
Here, between the critical years of AD 405-410, marked the real beginning of the end of the Western Empire. The spiral toward disintegration only gained momentum from there. But the seeds of this moment had been in the making for the last thirty years.
As we've seen, internal threats sapped the Western Empire's strength just as much as external ones. When it avoided debilitating civil wars, the unified Roman empire had successfully defended the frontiers for centuries. However, especially from the third century, the Empire's defenders had become a constant source of anxiety for rulers.
Usurpers leading battle-seasoned legions killed more emperors than foreign foes ever did. By the fifth century, every emperor knew this. That dynamic changed after the death of Theodosius I in AD 395.
After that, the empire would remain divided between east and west, with separate courts, bureaucracies, and armies. The two halves of the once-mighty Roman empire began going their different ways.
One usurper, Constantine III, led the legions out of Britain in AD 407 into Gaul to confront the barbarians who had entered the Empire at the end of AD 406. After some early victories, Constantine III was defeated and killed by a general of the Western Roman emperor, Honorius (AD 395-423). Still, Britain was now gone forever, the first in a series of dominoes that would topple in the coming decades.
In contrast, the Eastern Romans managed to avoid the kind of large-scale, regional civil strife that so weakened the West. Constantinople's overwhelming importance meant that those rare occasions of civil war in the East were short, sharp, struggles for control of the capital.  (NOTE: A good example of this was the brief civil war between Basiliscus and Zeno in AD 475-476. Control of the capital and its factions therein determined the ultimate victor.)
In the fifth century, you didn't see any rebellion from the eastern provinces far away from the capital. Again, I'd argue that this was because the axis of military, economic, and political power flowed decisively through Constantinople. If you wanted to rule the east, all roads led to the capital.
No other center of power could compete. In contrast, usurpers in the west took advantage of the fragmented power structures. Thus someone like Maximus Magnus or Constantine III could take over and govern the Roman provinces north of the Alps for years, often with no immediate challenge from the imperial government. Count Boniface could defy the western court in Ravenna from another rival power center in North Africa.
The wealthy western provinces of Gaul, Spain, and North Africa, were largely undefended once the Rhine and Danube were breached. Once that happened, the supine Western Emperors safely ensconced in Ravenna could do little but meow in response.
Rebellions like that of Constantine III in Britain and Gaul, Maximus of Hispania in Spain (AD 409-411), and Heraclianus in North Africa (AD 412-413) erupted because the inept court in Ravenna could not protect the provinces effectively. With the imperial center of gravity so lacking, the western regions gradually spun away from central control.
Once Vandals, Alans, Visigoths, Huns, and Ostrogoths were let loose within the Western Empire's undefended lands, a death spiral began. Each lost province meant fewer taxes; fewer taxes meant a reduced ability to mount a defense and sustain the state's necessary administrative functions. By the 470s, it was over. The Western Roman Empire had ceased to exist while the East would live on for another thousand years.
By the end of the fifth century, the crisis was passing. The Eastern Roman Empire was still standing, thanks to a narrow strip of water separating Europe from Asia and defended by the nearby imperial capital. The barbarian tribes that had dismantled the Western Empire were settling down and forming kingdoms: the Franks in Gaul; the Visigoths in Spain; the Vandals in Africa; and the Ostrogoths in Italy. The great age of the German Migrations was nearing an end, and Late Antiquity transitioned into the Early Middle Ages.
In the east, a dull, gray, 61-year old career bureaucrat named Anastasius I (AD 491-518) assumed the throne in AD 491. On the surface, it appeared an uninspired choice to select such a bland creature of the court.
But appearances can be deceiving. Anastasius showed energy that belied his age and used his administrative talents to implement long-overdue, but essential reforms of the empire's finances, army, and tax system. These reforms were not a moment too soon as hostilities resumed with Persia in AD 502 after a 60-year hiatus. Anastasius's reforms had taken root by then to such an extent that he could recruit 52,000 soldiers for the successful campaign in the east. 
The Eastern Roman army was back as a force to be reckoned with.
Not only that, but when Anastasius died in AD 518 at the ripe old age of 87, he left a staggering 120 tons of gold in the imperial treasury.  Not too shabby for a bland, elderly career bureaucrat. He was the perfect man to guide the ship of state out of the stormy fifth century.
The wheel of fortune turned. Someone far younger, energetic, and even more ambitious, would take that bursting treasury and set about reconquering the lost provinces of the former Roman west.
That man was Justinian, but that's a tale for another day.
Bryan Ward-Perkins. The Fall of Rome and the End of Civilization. Oxford University Press, 2007, 59.
Michael Grant. Constantine the Great: the Man and His Times. Scribner's, 1994, 120-122.
Edward Luttwak. The Grand Strategy of the Byzantine Empire. The Belknap Press of Harvard University Press, 2011, 72-73.
Edward Gibbon. The Decline and Fall of the Roman Empire. Modern Library, 2003, 495.
Ammianus Marcellinus. The Later Roman Empire (A.D. 354-378). Penguin Books, 2004, 443.
Warren Treadgold. A History of Byzantine State and Society. Stanford Univ. Press, 1997, 153.
Adrian Goldsworthy. The Fall of the West: the Slow Death of the Roman Superpower. Weidenfeld & Nicolson, 2009, 383.
J.B. Bury. From the Death of Theodosius I to the Death of Justinian. Dover, 1958, 275.
William Rosen. Justinian's Flea the First Great Plague and the End of the Roman Empire. Penguin Books, 2008.
Bury, J. B. From the Death of Theodosius I to the Death of Justinian. Dover, 1958.
Gibbon, Edward. The Decline and Fall of the Roman Empire. Modern Library, 2003.
Goldsworthy, Adrian Keith. The Fall of the West: the Slow Death of the Roman Superpower. Weidenfeld & Nicolson, 2009.
Grant, Michael. Constantine the Great: the Man and His Times. Scribner's, 1994.
Harper, Kyle. The Fate of Rome: Climate, Disease, and the End of an Empire. Princeton University Press, 2019.
Luttwak, Edward N. The Grand Strategy of the Byzantine Empire. The Belknap Press of Harvard University Press, 2011.
Marcellinus, Ammianus. The Later Roman Empire (A.D. 354-378). Penguin Books, 2004.
Rosen, William. Justinian's Flea the First Great Plague and the End of the Roman Empire. Penguin Books, 2008.
Treadgold, Warren T. A History of Byzantine State and Society. Stanford Univ. Press, 1997.
Ward-Perkins, Bryan. The Fall of Rome and the End of Civilization. Oxford University Press, 2007.