The future value of mitochondrial DNA (mtDNA) sequence information to studies in population biology will depend in part on understanding of mtDNA transmission genetics both within cell lineages and between animal generations. A series of stochastic models has been constructed here based on various possibilities concerning this transmission. Several of the models generate predictions inconsistent with available data and, hence, their assumptions are provisionally rejected. Other models cannot yet be falsified. These latter models include assumptions that (1) mtDNA's are sorted through cellular lineages by random allocation to daughter cells in germ cell lineages; (2) the effective intracellular population sizes (nM's) of mtDNA's are small; and (3) sperm may (or may not) provide a low level ‘gene-flow’ bridge between otherwise isolated female lineages. It is hoped that the models have helped to identify and will stimulate further empirical study of various parameters likely to strongly influence mtDNA evolution. In particular, critical experiments or measurements are needed to determine the effective sizes of mtDNA populations in germ (and somatic) cells and to examine possible paternal contributions to zygote mtDNA composition.