Mitochondrial DNA sequence variation is now being used to study the history of our species. In this paper we discuss some aspects of estimation and inference that arise in the study of such variability, focusing in particular on the estimation of substitution rates and their use in calibrating estimates of the time since the most recent common ancestor of a sample of sequences. Observed DNA sequence variation is generated by superimposing the effects of mutation on the ancestral tree of the sequences. For data of the type studied here, this ancestral tree has to be modeled as a random process. Superimposing the effects of mutation produces complicated sampling distributions that form the basis of any statistical model for the data. Using such distributions--for example, for maximum likelihood estimation of rates--poses some difficult computational problems. We describe a Monte Carlo method, a cousin of the popular "Markov chain Monte Carlo," that has proved very useful in addressing some of these issues.