The Romans made Greek literature and culture their own. They did this by adopting their stories in creative ways. Here are a few examples.
First, the Romans took over the Greek gods and added them to their pantheon of gods. Moreover, the Romans prided themselves on being the most pious people on earth. Cicero even says in his work,The Nature of the Gods the following words:
"If we wish to compare our [republic] to others, we will discover that in other things we are equal or inferior, but in religion, namely, the worship of the gods we are far superior."
Second, the Romans also took over Greek myths and created their own. For example, Livy is filled with pious legends.
Third, the Romans through military conquest also took over Greek learning. In fact, many of the Romans sent their children to places like Athens to study.
Fourth, the Romans also took over Greek forms of entertainment, such a plays. For example, the great Roman author, Plautus reinvented Greek comedy for a Roman audience.
Horace, an influential Latin poet, said:
Conquered Greece took captive her savage conqueror
and brought her arts into rustic Latium
These lines mean that even though Rome conquered Greece in the second century BC, and subsequently administered Greece as a province, Greek culture transformed Rome to an extraordinary degree. Many Roman authors describe this. Quinitilian, for example, complains that many wealthy Roman families became so concerned about their children learning Greek well that they hired Greek nurses and some young Roman children were actually more fluent in Greek than their own native Latin.
In the arts, many types of Greek culture supplanted indigenous Roman models. In theater, although the Latin mime tradition continued, most plays performed, including the the works of Plautus and Terence, were actually Latin translations of Greek New Comedy. Most Roman tragedies are adaptations of Greek ones such as the story of Medea. The great Roman epic, Virgil's Aeneid, was a continuation of Homer's Iliad, written in the identical meter (dactylic hexameter). A similar degree of influence can be seen in oratory (where Roman students studied Demosthenes and the other Attic orators) and lyric poetry.