The short answer is that Late Antiquity was a time of both foundation and decline. By the end of the fourth century C.E., the Eastern and Western portions of Rome’s empire were divided along linguistic, cultural, economic, and political lines. The fragmentation of Rome’s consolidated power left it vulnerable to attack from external enemies. Most famously, in 493-525, the Ostrogothic king Theodoric conquered Italy, significantly increasing the strength of Constantinople to influence the affairs of the old Roman Empire. The glory of the Roman Empire was at an end.
But this period also witnessed vast political and intellectual transformation both in the old Roman heartlands and in other world regions. In Rome proper, the most famous of these transformations came with the rise of Justinian (527-65), who was responsible for codifying Roman law and setting a precedent that all later Western code law would be based upon. The Byzantine (East Roman) Empire expanded from the Balkans down into eastern Turkey, and benefitted immensely by trade with the emergent Islamic empire and by the expansion of Byzantine scholarship. Byzantine academics studied the ancient Greek epics, including Homer, Plato, Thucydides, and Aristotle, and even learned much of the scientific literature that was coming out of the Islamic world at the time.
In Arabia, Muhammad (b. 570 in Mecca) was preparing to launch Islam onto the world stage. After his hijrah, or his pilgrimage from Mecca to Medina, Muhammad formed a strong, cohesive, and consolidated Islamic community, or umma. The Islamic umma proceeded to travel around the Arabian Peninsula and convert Bedouin tribes to Islam. After Muhammad’s death, his father-in-law, Abu-Bakr, facilitated the spread of the Muslim Empire into the West. By 750, the Umayyad caliphate could claim an empire that spread from the Arabian Penninsula, east to the edges of Persia, and westward, all across north Africa and into Al-Andalus of Spain. It was an incredibly productive time for the spread of Islam and the emergence of the new religious empire.
Late Antiquity also saw the rise of several initially small but powerful kingdoms on the periphery of the Old Roman empire, which would flourish in the subsequent centuries. In 862, according to the Russian Primary Chronicle, a group of tribesmen from central (current-day) Ukraine asked the Varangians to come and settle their capital city of Kiev. Rurik, the legendary first king of the Russians, acquiesced, and established the Rurikid dynasty in Kiev, leading to the birth of the Kievan Russian principality. Just north of Italy, the lands of Gaul also opened up to Viking invasion after the decline of Roman presence there. After a series of conflicts between the first Merovingian kings, the Frankish leader, Charlemagne, eventually built a strong military and bureaucracy in the territory, shifting the concentration of wealth and power tremendously in Gaul. Charlemagne – in German, “Charles the Great” – came to rule over a vast kingdom starting in 768. He was eventually crowned by the Pope himself. The Carolingian empire expanded all over current-day mainland France, and, according to the Frankish epic The Song of Roland, successfully campaigned against the Saracen kings in northeastern Spain.
Thus, even though Europe saw the decline of perhaps the most formidable of empires of the ancient world, Rome’s decline precipitated the rise of many new groups of peoples and successful kingdoms.