Mitochondria form dynamic networks in the cell that are balanced by the flux of iterative fusion and fission events of the organelles. It is now appreciated that mitochondrial fission also represents an end-point event in a signalling axis that allows cells to sense and respond to external cues. The fission process is orchestrated by membrane-associated adaptors, influenced by organellar and cytoskeletal interactions and ultimately executed by the dynamin-like GTPase DRP1. Here we invoke the framework of the 'mitochondrial divisome', which is conceptually and operationally similar to the bacterial cell-division machinery. We review the functional and regulatory aspects of the mitochondrial divisome and, within this framework, parse the core from the accessory machinery. In so doing, we transition from a phenomenological to a mechanistic understanding of the fission process.