For most eukaryotic organisms, the nuclear genomes of both parents are transmitted to the progeny following biparental inheritance. For mitochondria and chloroplasts, however, uniparental inheritance (UPI) is frequently observed. The maternal mode of inheritance for mitochondria in animals can be nearly absolute, suggesting an adaptive advantage for UPI. In other organisms, however, the mode of inheritance for mitochondria and chloroplasts can vary greatly even among strains of a species. Here, I review the data on the transmission of organellar DNA (orgDNA) from parent to progeny and the structure, copy number, and stability of orgDNA molecules. I propose that UPI is an incidental by-product of DNA abandonment, a process that lowers the metabolic cost of orgDNA repair.