Cellular degradative processes including proteasomal and vacuolar/lysosomal (autophagic) degradation, as well as the activity of proteases (both cytosolic and mitochondrial), provide for a continuous turnover of damaged and obsolete macromolecules and organelles. Mitochondria are organelles essential for respiration and oxidative energy production in aerobic cells; they are also required for multiple biosynthetic pathways. As such, mitochondrial homeostasis is very important for cell survival. We review the evidence regarding the possible mechanisms for mitochondrial degradation. Increasingly, the evidence suggests autophagy plays a central role in the degradation of mitochondria. How mitochondria might be specifically selected for autophagy (mitophagy) remains an open question, although some evidence suggests that, under certain circumstances, in mammalian cells the Mitochondrial Permeability Transition (MPT) plays a role in initiation of the process. As more is learned about the functioning of autophagy as a degradation process, the greater the appreciation we are developing concerning its role in the control of mitochondrial degradation.