The mitochondrion is an organelle that carries out a number of important metabolic processes such as fatty acid oxidation, the citric acid cycle, and oxidative phosphorylation. However, this multitasking organelle also generates reactive oxygen species (ROS), which can cause oxidative stress resulting in self-damage. This type of mitochondrial damage can lead to the further production of ROS and a resulting downward spiral with regard to mitochondrial capability. This is extremely problematic because the accumulation of dysfunctional mitochondria is related to aging, cancer, and neurodegenerative diseases. Accordingly, appropriate quality control of this organelle is important to maintain proper cellular homeostasis. It has been thought that selective mitochondria autophagy (mitophagy) contributes to the maintenance of mitochondrial quality by eliminating damaged or excess mitochondria, although little is known about the mechanism. Recent studies in yeast identified several mitophagy-related proteins, which have been characterized with regard to their function and regulation. In this article, we review recent advances in the physiology and molecular mechanism of mitophagy and discuss the similarities and differences of this degradation process between yeast and mammalian cells.