Final answer:
Theodora and Justinian governed the Byzantine Empire, which saw its greatest expansion and cultural achievements during Justinian's reign from 527-565 AD.
Step-by-step explanation:
The empire that Empress Theodora and Emperor Justinian governed is known as the Byzantine Empire. This empire reached its peak under Justinian's rule from 527 to 565 AD. They oversaw significant territorial expansions, legal reforms, and cultural achievements, including the building of the renowned Hagia Sophia in Constantinople, and they exerted considerable influence on both the spiritual and secular aspects of the Empire.
The Byzantine Empire covered extensive areas including the Balkans, North Africa, Anatolia, the Levant, Italy, and the southern Iberian Peninsula at its zenith. Despite external pressures from neighboring powers such as the Persian Empire, the Byzantines managed to maintain control over these regions by setting up exarchates, military provinces ruled by exarchs. After Justinian's reign, Byzantine influence gradually receded due to various invasions and internal challenges, although the Empire endured in a smaller form for many centuries.