Mitochondria are critical for supplying energy to the cell, but during catabolism this organelle also produces reactive oxygen species that can cause oxidative damage. Accordingly, quality control of mitochondria is important to maintain cellular homeostasis. It has been assumed that autophagy is the pathway for mitochondrial recycling, and that the selective degradation of mitochondria via autophagy (mitophagy) is the primary mechanism for mitochondrial quality control, although there is little experimental evidence to support this idea. Recent studies in yeast identified several mitophagy-related genes and have uncovered components involved in the molecular mechanism and regulation of mitophagy. Similarly, studies of Parkinson disease and reticulocyte maturation reveal that Parkin and Nix, respectively, are required for mitophagy in mammalian cells, and these analyses have revealed important physiological roles for mitophagy. Here, we review the current knowledge on mitophagy, in particular on the molecular mechanism and regulation of mitophagy in yeast. We also discuss some of the differences between yeast and mammalian mitophagy.