Mitochondrial DNA (mtDNA) is a pivotal tool in molecular ecology, evolutionary and population genetics. The power of mtDNA analyses derives from a relatively high mutation rate and the apparent simplicity of mitochondrial inheritance (maternal, without recombination), which has simplified modelling population history compared to the analysis of nuclear DNA. However, in biology things are seldom simple, and advances in DNA sequencing and polymorphism detection technology have documented a growing list of exceptions to the central tenets of mitochondrial inheritance, with paternal leakage, heteroplasmy and recombination now all documented in multiple systems. The presence of paternal leakage, recombination and heteroplasmy can have substantial impact on analyses based on mtDNA, affecting phylogenetic and population genetic analyses, estimates of the coalescent and the myriad of other parameters that are dependent on such estimates. Here, we review our understanding of mtDNA inheritance, discuss how recent findings mean that established ideas may need to be re-evaluated, and we assess the implications of these new-found complications for molecular ecologists who have relied for decades on the assumption of a simpler mode of inheritance. We show how it is possible to account for recombination and heteroplasmy in evolutionary and population analyses, but that accurate estimates of the frequencies of biparental inheritance and recombination are needed. We also suggest how nonclonal inheritance of mtDNA could be exploited, to increase the ways in which mtDNA can be used in analyses.