Mitochondrial fission is important for many aspects of cellular homeostasis, including mitochondrial distribution, stress response, mitophagy, mitochondrially derived vesicle production and metabolic regulation. Several decades of research has revealed much about fission, including identification of a key division protein - the dynamin Drp1 (also known as DNM1L) - receptors for Drp1 on the outer mitochondrial membrane (OMM), including Mff, MiD49 and MiD51 (also known as MIEF2 and MIEF1, respectively) and Fis1, and important Drp1 regulators, including post-translational modifications, actin filaments and the phospholipid cardiolipin. In addition, it is now appreciated that other organelles, including the endoplasmic reticulum, lysosomes and Golgi-derived vesicles, can participate in mitochondrial fission. However, a more holistic understanding of the process is lacking. In this Review, we address three questions that highlight knowledge gaps. First, how do we quantify mitochondrial fission? Second, how does the inner mitochondrial membrane (IMM) divide? Third, how many 'types' of fission exist? We also introduce a model that integrates multiple regulatory factors in mammalian mitochondrial fission. In this model, three possible pathways (cellular stimulation, metabolic switching or mitochondrial dysfunction) independently initiate Drp1 recruitment at the fission site, followed by a shared second step in which Mff mediates subsequent assembly of a contractile Drp1 ring. We conclude by discussing some perplexing issues in fission regulation, including the effects of Drp1 phosphorylation and the multiple Drp1 isoforms.