The utility of whole-genome sequencing for pathogens, and how informative sequence data are for outbreaks, remains unknown, and is important as public health systems around the world decide how much sequencing to undertake for infectious disease surveillance. In this talk, I introduce an MCMC method for simultaneous reconstruction of phylogenetic trees and transmission trees using sequence data for a person-to-person outbreak of an infectious disease. The method is called BREATH: Bayesian Reconstruction and Evolutionary Analysis of Transmission Histories. BREATH's transmission process accounts for a flexible natural history of infection (including a latent period if desired) and a separate process for sampling. It allows for unsampled individuals and for individuals to have diverse within-host infections. BREATH also accounts for the fact that an outbreak may still be ongoing at the time of analysis, using a recurrent events approach to account for right truncation. We perform a simulation study to verify our implementation, and apply BREATH to a previously-described 13-year outbreak of tuberculosis. We find that using a transmission process to inform the phylogenetic reconstruction results in better resolution of the phylogeny (in topology, branch length and tree height) and a more precise estimate of the time of origin of the outbreak. But even with whole-genome sequence data, considerable uncertainty remains about transmission events. An open source implementation of BREATH is available from https://github.com/rbouckaert/transmission as the BREATH package to BEAST 2.