Lots of things really. In the mid-Empire, the vast majority became citizens after emperor Caracalla issued an edict in AD 212. Even prior to that, since the reign of Caesar many non-Roman peoples were being included in the Senate.

Regarding governance, during Imperial Rome there were Senatorial Provinces and Imperial ones. Senatorial provinces were ran by a senator, and Imperial provinces were ran by someone chosen by the emperor.

For religion, for the most part, everything largely remained the same until Constantine as local gods underwent syncretism, which is basically combining the local and the Roman god.

In earlier times, defeated people were often incorporated into the Roman army, and this was still somewhat sought after as it guaranteed citizen during a time when it was hard to achieve.

There are some nuances that I did not cover, but this is the basic way the provinces changed. If you fancy some reading on the early empire, try Suetonius' Lives of the Twelve Caesars, which an enjoyable biographical look at the first 11 emperors (and Julius Caesar).