Concurrent mitochondrial elimination and autophagy in many systems has led to the proposal that autophagy is the main mechanism of mitochondrial turnover during development and under pathological conditions. The term mitophagy was coined to describe the selective removal of mitochondria by autophagy but the process itself is still contentious. Three questions are being debated: 1) Is there a specific removal of mitochondria by autophagy or is it non-selective or inadvertent? 2) What are the signals that drive this process? 3) Does removal of mitochondria increase or decrease cell viability? There is a mounting evidence for specific signals in/on mitochondria that drive mitochondrial removal from cells by autophagy. The process itself may be both selective and non-selective. In yeast, surprisingly, mitochondrial elimination occurs more by microautophagy (intracellular pinocytosis by the vacuolar membrane) than macroautophagy (initiated by stand-alone nascent double membrane structures known as autophagosomes). In mammalian cells, macroautophagy seems most prevalent though tools to study microautophagy are not well developed. Whilst lack of mitophagy seems to be deleterious, understanding the interplay between autophagy, mitochondrial performance, and cell pathology is a much-needed area of research.