Horace famously said that "Captive Greece captured her rude conqueror." By this he meant that although Rome succeeded in its military conquest of Greece, in doing so, it adapted Greek culture to a striking degree. In education, for example, aristocratic parents would hire Greek slaves as paedogogi so that their sons would do better at learning Greek, a practice so widespread that some aristocratic Romans were more fluent in Greek than in Latin. Wealthy young men would head to Greece or Alexandria to learn philosophy and rhetoric.
In architectural terms, this meant that Roman temples and many other buildings were built in the style of Greek ones and many cults and religious practices were imported from Greece or assimilated to Greek exemplars. Rome became more heavily urbanized during this period and more dependent upon slave labor.
During this period, Rome evolved from Republic to Empire, emulating the administrative models of the vast Hellenistic empires, growing larger and more complex bureaucracies and relying on conquest and colonization for revenue. In terms of problems, Rome developed vast slums and became dependent not just on its own periphery but also Egypt for its food. The transition from Republic to Empire and the increasingly "oriental" model for the monarchy led to many forms of abuse of power.