Abstract Eukaryotes likely originated from an endosymbiosis between an α-protobacterium and an Asgard archaeal host. Although endosymbiosis was followed by massive gene transfer from the mitochondrial DNA (mtDNA) to the nuclear genome, mtDNA was retained in most eukaryotes. Since the early 1980s, the genetic variation, species diversity and functional implications of mtDNA’s genetic content have been extensively studied. Here, we assemble articles that discuss recent advances and new insights into mitochondrial evolution. In this introductory article, we begin by discussing the origin of mtDNA and the mechanisms that maintain the integrity of the mitochondrial and nuclear genomes. We then discuss the importance of asymmetry in communication between the two genomic partners in the context of sequestration of the archaeal genome in a nuclear compartment. Given the putative initial biparental inheritance of the multi-copy mtDNA in the absence of mitosis and meiosis-like mechanisms that control mtDNA segregation, we next discuss selection against selfish mtDNA. When considering the selective advantage and time frame for the emergence of uniparental mtDNA transmission, we ask how the evolution of uniparental inheritance is associated with the evolution of sexes and early germline sequestration. Finally, we analyse the possible expansion of mtDNA genetic content and its impact on the functional and evolutionary dynamics of mitochondria. We conclude by considering mito-nuclear coevolution and interaction. This article is part of the theme issue ‘Evolutionary genetics of mitochondria: on diverse and common evolutionary constraints across eukarya’.