It's a whole separate life cycle linked, but independent. They're constantly dividing like bacteria (but in a way that's initiated by the parent cell) and fusing together. Over time, damaged mitochondria accumulate and are selectively degraded.

They (still) have their own DNA, their own DNA replication, repair, transcription and translational machinery to make proteins. Interestingly, the proteins they make start with the same amino acid that bacterial ones do, so, if you get an injury that releases a lot of mitochondria into your circulation, your immune system recognises it as an infection. This can kill you.