Until very recently, mitochondria were thought to be clonally inherited through the maternal line in most higher animals. However, three papers published in 2000 claimed population–genetic evidence of recombination in human mitochondrial DNA. Here I review the current state of the debate. I review the evidence for the two main pathways by which recombination might occur: through paternal leakage and via a mitochondrial DNA sequence in the nuclear genome. There is no strong evidence for either pathway, although paternal leakage seems a definite possibility. However, the population–genetic evidence, although not conclusive, is strongly suggestive of recombination in mitochondrial DNA. The implications of non–clonality for our understanding of human and mitochondrial evolution are discussed.