Mitochondria are best known for their role in the generation of ATP by aerobic respiration. Yet, research in the past half century has shown that they perform a much larger suite of functions and that these functions can vary substantially among diverse eukaryotic lineages. Despite this diversity, all mitochondria derive from a common ancestral organelle that originated from the integration of an endosymbiotic alphaproteobacterium into a host cell related to Asgard Archaea. The transition from endosymbiotic bacterium to permanent organelle entailed a massive number of evolutionary changes including the origins of hundreds of new genes and a protein import system, insertion of membrane transporters, integration of metabolism and reproduction, genome reduction, endosymbiotic gene transfer, lateral gene transfer and the retargeting of proteins. These changes occurred incrementally as the endosymbiont and the host became integrated. Although many insights into this transition have been gained, controversy persists regarding the nature of the original endosymbiont, its initial interactions with the host and the timing of its integration relative to the origin of other features of eukaryote cells. Since the establishment of the organelle, proteins have been gained, lost, transferred and retargeted as mitochondria have specialized into the spectrum of functional types seen across the eukaryotic tree of life.