I will describe a Bayesian approach to reconstructing who infected whom with the help of pathogen genetic data. As sequencing technologies have dramatically declined in cost, it is now feasible to sequence large numbers of viral or bacterial genomes in infectious disease outbreaks, and there have been high hopes that the resulting DNA or RNA sequences will tell the story of who infects whom and when, leading to both better infectious disease control and a better understanding of pathogen evolution. However, sequences do not directly reveal who infected whom, and leave considerable uncertainty. I will outline our main approach with extensions to include multiple datasets and to handle covariates. Finally I will describe the limitations, and several open challenges in this area.