The inheritance of mitochondrial and chloroplast genes differs from that of nuclear genes in showing vegetative segregation, uniparental inheritance, intracellular selection, and reduced recombination. Vegetative segregation and some cases of uniparental inheritance are due to stochastic replication and partitioning of organelle genomes. The rate and pattern of vegetative segregation depend partly on the numbers of genomes and of organelles per cell, but more importantly on the extent to which genomes are shared between organelles, their distribution in the cell, the variance in number of replications per molecule, and the variance in numerical and genotypic partitioning of organelles and genomes. Most of these parameters are unknown for most organisms, but a simple binomial probability model using the effective number of genomes is a useful substitute. Studies using new cytological, molecular, and genetic methods are shedding some light on the processes involved in segregation, and also on the mechanisms of intracellular selection and uniparental inheritance in mammals. But significant issues remain unresolved, notably about the extent of paternal transmission and mitochondrial fusion in mammals.