The Byzantine Empire is the eastern section of the Roman Empire which remained in existence after the fall of the western section. After the conquest of Rome the East Roman Empire was commonly referred to as the Byzantine Empire after the original name of its capital city, Byzantium. The Roman emperor Constantine the Great rebuilt the city in AD 330 and called it Constantinople (today's Istanbul). The Byzantines referred to themselves as Romans. After the division of the empire (AD 395) into eastern and western territories during the reign of emperor Arcadius, Constantinople became the capital of the East Roman Empire.
The Eastern Empire was largely spared the difficulties of the west in the 3rd and 4th centuries, in part because urban culture was better established there and the initial invasions were attracted to the wealth of Rome. By the 6th century it had reestablished itself and under Justinian I reconquered much of Italy, north Africa, and Spain.
Justinian left his successors an empty treasury, however, and they were unable to deal with the sudden appearance of new invaders on all fronts. The Lombards took Italy, the Khazars overwhelmed much of the Balkans, and the Persians gained domination of most of the eastern provinces. These were recovered by the emperor Heraclius, who annihilated the Sassanid kingdom, but the sudden appearance of the Arabs was too much for the empire, and the southern provinces were all overrun.
What the empire lost in territory, though, it made up in uniformity. The southern provinces differed significantly from the northern in culture and practiced monophysite (rather than orthodox) Christianity, and so felt alienated; the north put up much more of a struggle. By the time of Heraclius the empire had become a Greek rather than Roman empire, and had been divided into a system of military provinces called themes to face permanent assault, with urban life declining outside the capital while it grew to become the largest city in the world. Attempts to conquer Constantinople failed in the face of the Byzantine's superior navy, and the empire began to recover.
The empire reached its height under the Macedonian emperors of the 10th and early 11th centuries. As Rome before it had, though, it soon fell into a period of difficulties, caused to a large extent by the growth of landed aristocracy, which undermined the theme system. Faced off against its old enemies, the Holy Roman Empire and the Abbasid caliphate, it may have recovered, but around the same time new invaders appeared on the scene who had little reason to respect its reputation - the Normans, who conquered Italy, and the Seljuk Turks, who were mainly interested in defeating Egypt but still made moves into Asia Minor, the main recruiting ground for the Byzantine armies. With the defeat at Manzikert of emperor Romanus IV in 1071 by Alp Arslan, sultan of the Seljuk Turks, that province was lost.
The last few centuries of Byzantine life were brought by an usurper, Alexius Comnenus, who began to reestablish an army on the basis of feudal grants (pronoia) and made significant advances against the Seljuk Turks. His plea for western aid brought about the first crusade, which helped him reclaim Nicaea but soon distanced itself from imperial aid. Later crusades grew increasingly antagonistic and in 1204 the Fourth Crusade captured Constantinople, founding a short-lived feudal kingdom and permanently weakening Byzantine power.
Three Byzantine successor states were left - Nicaea, Epirus, and Manzikert. The first managed to reclaim Constantinople and defeat Epirus under the Palaeologian dynasty, so reviving the empire but turning attention to Europe when Asia was the primary concern. For a while the empire survived simply because the Muslims were too divided to attack, but eventually the Ottomans overran all but a handful of port cities. Constantinople was initially considered not worth the effort, but with the advent of cannons it fell after a two year siege to Mehmed II in 1453. By the end of the century the remaining cities - like Trebizond and Mistra - also fell.
The Byzantine empire played an important role in the transmission of Roman knowledge to the Islamic world. Its most lasting influence, though, lies in its church. Early Byzantine missionary work spread Orthodox Christianity to various Slavic peoples, and it is still predominant among them and the Greeks. The start and end dates of the capital's independence, 395 to 1453, were the originally defined bounds of the Middle Ages.