Mitochondria autophagy (mitophagy) is a process that selectively degrades mitochondria via autophagy. Recently, there has been significant progress in the understanding of mitophagy in yeast. Atg32, a mitochondrial outer membrane receptor, is indispensable for mitophagy. Phosphorylation of Atg32 is an initial cue for selective mitochondrial degradation. Atg32 expression and phosphorylation regulate the induction and efficiency of mitophagy. In addition to Atg32-related processes, recent studies have revealed that mitochondrial fission and the mitochondria-endoplasmic reticulum (ER) contact site may play important roles in mitophagy. Mitochondrial fission is required to regulate mitochondrial size. Mitochondria-ER contact is mediated by the ER-mitochondria encounter structure and is important to supply lipids from the ER for autophagosome biogenesis for mitophagy. Mitophagy is physiologically important for regulating the number of mitochondria, diminishing mitochondrial production of reactive oxygen species, and extending chronological lifespan under caloric restriction. These findings suggest that mitophagy contributes to maintain mitochondrial homeostasis. However, whether mitophagy selectively degrades damaged or dysfunctional mitochondria in yeast is unknown. This article is part of a Special Issue entitled: Mitophagy. (C) 2015 Elsevier B.V. All rights reserved.