Mitochondria produce energy in the form of ATP via oxidative phosphorylation. As defects in oxidative phosphorylation can generate harmful reactive oxygen species, it is important that damaged mitochondria are efficiently removed via a selective form of autophagy known as mitophagy. Owing to a combination of cell biological, structural and proteomic approaches, we are beginning to understand the mechanisms by which ubiquitin-dependent signals mark damaged mitochondria for mitophagy. This Review discusses the biochemical steps and regulatory mechanisms that promote the conjugation of ubiquitin to damaged mitochondria via the PTEN-induced putative kinase 1 (PINK1) and the E3 ubiquitin-protein ligase parkin and how ubiquitin chains promote autophagosomal capture. Recently discovered roles for parkin and PINK1 in the suppression of mitochondrial antigen presentation provide alternative models for how this pathway promotes the survival of neurons. A deeper understanding of these processes has major implications for neurodegenerative diseases, including Parkinson disease, where defects in mitophagy and other forms of selective autophagy are prominent.