It has been proposed that age-dependent accumulation of somatic mutations in mtDNA is responsible for some aspects of the aging process. However, most cells contain hundreds to thousands of mtDNA molecules. Any nascent somatic mutant therefore appears as a single copy among a majority of wild-type species. A single mutant molecule is unlikely to influence the physiology of the cell and thus cannot play a role in the aging process. To affect cellular physiology, the nascent somatic mutants must somehow accumulate clonally in the cell to significant levels. The evidence supporting the view that, indeed, clonal expansion of mtDNA mutations is a widespread process in various human tissues, and the mechanisms by which clonal expansions may affect the aging process, are reviewed. Originally, clonal expansion was demonstrated for mtDNA with large deletions in muscle. Cell-by-cell analysis of human cardiomyocytes and buccal epithelial cells revealed that clonal expansion affects point mtDNA mutations as well as deletions. Expansions are not limited to muscle, but likely are present in most tissues, and almost every cell of an aged tissue is likely to be affected by an expansion. While the very existence of clonal expansion is beyond doubt, the mechanisms driving this process are largely controversial. The hypotheses explaining expansion includes random or various selective mechanisms, or both. We show that the spectra of expanded point mutations are drastically different in cardiomyocytes and epithelial cells. This suggests that the mechanisms of expansion in these tissues are different. In particular, we propose random segregation and positive selection models for epithelial and muscle cells, respectively.