During the period of the Eastern Roman Empire, the Crimean territory served as a critical trade post for the northern Black Sea, but also served a crucial secondary purpose as a forward lookout position for any of the various warlike migratory tribes that would be making their way west or south towards the Empire. Grand Prince Vladimir I of Kiev took the major city of Chersonesos in Crimea hostage in 988 to force Emperor Basil II to not renege on his agreement to wed his sister Anna to the Grand Prince, after the latter helped him put down a revolt the prior year. Considering that an imperial princess had never been wed to a foreigner before this point and Basil ended up agreeing to the marriage after the takeover, you can imagine how important this strategic province was to the Empire (although this ended up with a welcome side-purpose of finalizing Vladimir's conversion to the Orthodox Church, followed swiftly by the rest of his people).

Source: J.J. Norwich, "History of Byzantium"

During the Classical period, the region was called Chersonesus, which was also the main city. Its history as a Greek colony stretches back into the classical or late Archaic, founded as part of the general movement of Greeks around the Mediterranean, and it came into the Roman orbit during the process of the Roman conquest of the interior of Asia Minor. It was never really under full control of the Romans, but had had a fairly long history of trading some of its sovereignty in exchange for protection from its troublesome northern frontier. During the third century it capitulated to the Goths and was a major source of their naval power.

The inhabitants were Greek colonists, but the Black Sea Greek colonies in general tended to be very heavily mixed with the "indigenous" populations. Economically, it was a very fertile agricultural region and major exporter of grain.