Mitochondrial quality is a crucial determinant of cell viability, and mitochondrial autophagy plays a central role in this control mechanism. Based on studies in yeast, numerous investigations of this process have been conducted, and the framework of mammalian mitochondrial autophagy is progressively appearing. However, many enigmas about the molecular mechanisms involved remain unsolved. Furthermore, the pathological significance of mitochondrial autophagy in the heart remains largely unclear. In this review, we discuss the current understanding of mitochondrial autophagy in mammals with reference to that in yeast. Regarding the process in yeast, some points of uncertainty have arisen. We also summarize recent advances in the research of autophagy and mitochondrial autophagy in the heart. This article is a part of a review series on Autophagy in Health and Disease.