A far flung part of your empire would secede if corruption or something is too high or too bad. They would share the same culture as yourself, naturally, but they would have a new leader head, and have a bad attitude towards you (if you let them go, they'll think you're weak; if you attack them, they'll hate you). Captured culture improvements would not be destroyed, because you're the same culture.
The atrocities would work just like SMAC, with certain actions declared atrocities and you take a rep hit if you committ them. Also there will be international reprisal, especially from civs in representative governments. Civs that have committed similiar atrocities are likely to look the other way.