Heteroplasmy occurs when copies of an organellar genome (plastid or mitochondrial) differ from one another either within a cell or among cells within an individual. This phenomenon was first discovered in plastids over 100 years ago, though ‘heteroplasmy’ was not formally defined until decades later. Mitochondrial and plastid heteroplasmy have since been discovered in diverse taxa, including numerous plants, particularly those with the gynodioecious breeding system. Though heteroplasmy can arise through mutations in organellar genomes, biparental inheritance of organelles often generates heteroplasmy. This article is intended to summarise the cytoploid nature of organellar genomes and different aspects of mitochondrial and plastid heteroplasmy, from its discovery, to the development of detection methods. We will also discuss the effects of heteroplasmy on individuals, populations, and species, with regard to fitness, cytonuclear interactions, and genome evolution. Finally, we highlight a few research questions which we consider in need of further investigation to understand the prevalence and effects of heteroplasmy in natural settings.