Genomic data is becoming increasingly important to understand the spread of infectious diseases. The diversity in genomic datasets reflects the phylogenetic relationships between isolates, but this phylogeny is not directly informative about who infected whom, due to the presence for many infectious pathogens of extensive within-host evolution and diversity. We have recently shown that phylogenies can be interpreted in terms of the underlying transmission tree by “colouring” the branches of the phylogeny with a unique colour for each host. This two steps approach of first constructing a phylogeny and then “converting” it into a transmission tree will be briefly reviewed, as well as its pros and cons. This method is however currently limited because it requires that all cases are sampled and that the outbreak is finished, assumptions that are rarely met in practice. We will present extensions of the method that allow us to remove these limitations for a large class of epidemiological models. The resulting algorithm is a reversible jump Monte-Carlo Markov Chain which should be applicable in many practical situations.