In addition to their nuclear genome, eukaryotic organisms carry multiple asexual mitochondrial genomes. Lacking recombination, asexual genomes should struggle to accumulate beneficial substitutions and to purge those that are deleterious. Yet, empirical evidence of adaptive evolution in mitochondria suggests that they suffer none of these limitations of asexual reproduction. Here I use a computational model to show that the unique biology of mitochondrial genomes—in particular their large copy number combined with uniparental inheritance—enable them to readily undergo adaptive evolution. Uniparental inheritance increases variation in fitness between individuals, selecting against individuals with a high deleterious substitution load and for individuals that carry multiple beneficial substitutions. I will show that uniparental inheritance decreases competition between different beneficial substitutions (clonal interference), reduces genetic hitchhiking of deleterious substitutions during selective sweeps, and promotes adaptive evolution by increasing the level of beneficial substitutions relative to deleterious substitutions. When assuming that mitochondria inherit biparentally, the presumed ancestral state, decreasing the number of genomes transmitted during gametogenesis (transmission bottleneck) aids adaptive evolution. However, uniparental inheritance is required to maintain variation in fitness between individuals on which selection can act. As a result even a tight transmission bottleneck combined with biparental inheritance leads to less efficient adaptive evolution than when inheritance is uniparental. These findings explain the empirical observations that mitochondria—despite their asexual mode of reproduction—can readily accumulate beneficial substitutions and resist the accumulation of deleterious substitutions.