Mitochondria, a nearly ubiquitous feature of eukaryotes, are derived from an ancient symbiosis. Despite billions of years of cooperative coevolution — in what is arguably the most important mutualism in the history of life — the persistence of mitochondrial genomes also creates conditions for genetic conflict with the nucleus. Because mitochondrial genomes are present in numerous copies per cell, they are subject to both within- and among-organism levels of selection. Accordingly, ‘selfish’ genotypes that increase their own proliferation can rise to high frequencies even if they decrease organismal fitness. It has been argued that uniparental (often maternal) inheritance of cytoplasmic genomes evolved to curtail such selfish replication by minimizing within-individual variation and, hence, within-individual selection. However, uniparental inheritance creates conditions for cytonuclear conflict over sex determination and sex ratio, as well as conditions for sexual antagonism when mitochondrial variants increase transmission by enhancing maternal fitness but have the side-effect of being harmful to males (i.e., ‘mother's curse’). Here, we review recent advances in understanding selfish replication and sexual antagonism in the evolution of mitochondrial genomes and the mechanisms that suppress selfish interactions, drawing parallels and contrasts with other organelles (plastids) and bacterial endosymbionts that arose more recently. Although cytonuclear conflict is widespread across eukaryotes, it can be cryptic due to nuclear suppression, highly variable, and lineage-specific, reflecting the diverse biology of eukaryotes and the varying architectures of their cytoplasmic genomes. Havird et al. explain how mitochondrial and nuclear genomes can come into conflict with one another and how this fits into specific features of organelle/host biology, such as the commonly observed uniparental inheritance of mitochondria.