Greek language and literature enjoyed considerable status among Roman optimates during the republic and after. Cicero himself did not disdain to translate treatises into Latin.
But in late antiquity, as the centre of Roman government moved to Constantinople, there began to be a need to translate in the other direction. I must say that I have never known much about this.
One instance of this process is material quoted by Eusebius. Little of this is from Latin sources, but he makes use of a translation into Greek of Tertullian’s Apologeticum. In other places he quotes imperial edicts, evidently from official translations. But he does not seem to have known much Latin himself.
Another instance is material by Jerome. Jerome himself tells us that his Life of St. Hilarion was translated into Greek by a certain Sophronius. His De viris illustribus was translated into Greek by ps.Sophronius, and the version is extant. Interesting the version of the Testimonium Flavianum given by Jerome features the crucial variant, He was believed to be the Christ (credebatur esse Christum). But in the Greek version the text has been harmonised to the normal Greek text, He was the Christ.
All these things are something I would like to know more about. Today I stumbled across a volume on Google books, extant in preview mode, John J. Winkler &c, Later Greek Literature (1982). This is a collection of essays, but includes on p.173-216 a paper by Elizabeth Fisher, Greek translations of Latin Literature in the fourth century. This discusses in a very interesting way some of these examples, and shows precisely how the translator handled his material.
Sometimes this was with considerable freedom. Jerome’s negative portrayal of Alexander was modified for a Greek audience, where the latter’s hero-status could not be ignored, for instance.
Much of the article is visible through Google Books, and is worth a look.