Final answer:
The late Roman and early Byzantine empires faced challenges such as military threats from external forces like the Islamic armies and Turkic tribes, internal power struggles with wealthy elites, and the schism between the western and eastern churches.
Step-by-step explanation:
The late Roman and early Byzantine empires faced several principal challenges including external military threats, internal power struggles, and societal transformations. One of the significant external challenges was the rise of the Islamic forces to the south, which eventually led to significant losses of territory for the Byzantines, including North Africa and the eastern Mediterranean coast. The Byzantine Empire also contended with the invasions of migratory peoples from the north and east, which included various Turkic tribes, especially the Seljuks, who weakened the empire's control over its eastern provinces.
Internally, the Byzantine Empire struggled with the rising power of wealthy aristocrats, known as the dynatoi, who sought to exploit the weaknesses of the government to enrich themselves. This internal strife weakened the societal structure, including the military, further compromising the empire's ability to defend its borders. Additionally, the Byzantines experienced the schism between the western and eastern Christian churches, which added to the socio-religious challenges during this era.