Recent biochemical and molecular-genetic discoveries concerning variations in human mtDNA have suggested a role for mtDNA mutations in a number of human traits and disorders. Although the importance of these discoveries cannot be emphasized enough, the complex natures of mitochondrial biogenesis, mutant mtDNA phenotype expression, and the maternal inheritance pattern exhibited by mtDNA transmission make it difficult to develop models that can be used routinely in pedigree analyses to quantify and test hypotheses about the role of mtDNA in the expression of a trait. In the present paper, we describe complexities inherent in mitochondrial biogenesis and genetic transmission and show how these complexities can be incorporated into appropriate mathematical models. We offer a variety of likelihood-based models which account for the complexities discussed. The derivation of our models is meant to stimulate the construction of statistical tests for putative mtDNA contribution to a trait. Results of simulation studies which make use of the proposed models are described. The results of the simulation studies suggest that, although pedigree models of mtDNA effects can be reliable, success in mapping chromosomal determinants of a trait does not preclude the possibility that mtDNA determinants exists for the trait as well. Shortcomings inherent in the proposed models are described in an effort to expose areas in need of additional research.