A rapid increase in the amount of available pathogen genetic data, which is ongoing and likely to continue for the foreseeable future, presents new opportunities and challenges in molecular epidemiology, and in the emerging field of “phylodynamics”, which seeks to unify the study of the evolutionary and epidemiological dynamics of pathogen populations. This thesis explores some of these challenges and opportunities, with a focus on pathogens infecting livestock and poultry. I conducted analyses of sequences from two serotypes of foot-and-mouth-disease virus (FMDV) in order to investigate the global population dynamics of the virus. For serotype SAT 2, the amount of publicly available genomic data is still small enough that all of it could be included in a single analysis. A particular focus was the origins of historical outbreaks occurring in North Africa and the Middle East, outside the endemic area for the serotype. The results suggested sources for these in countries just south of the Sahara, and that the viruses responsible for three outbreaks occurring in 2012 were the result of separate introductions. For serotype O, including every available sequence was not feasible and the data had to be sub-sampled. Little research has been conducted on how to design a sampling strategy for sequence analysis of pathogens, an issue of increasing importance, so a simulation study was conducted to identify one. This suggested that, when reconstructing the temporal and spatial dynamics of a structured population of pathogens or infected individuals, it is preferable to stratify by subpopulation and by time period. The type O analysis itself showed that the south-east Asian topotype moves between countries according to cattle trade networks, but that geographic proximity is also important for strains from southern Asia and the Middle East. With genetic data available at an epidemiological resolution that was previously inconceivable, there are opportunities for new types of inference. For example, if we can acquire a sequence from all or most infected cases in an epidemic, they can inform inference of who infected who, complementing traditional contact-tracing approaches. I introduce a novel phylodynamic method for the simultaneous reconstruction of phylogeny and transmission tree for an epidemic in a situation where every infected host or premises can be identified and a sequence acquired from most of them. The performance of this method was demonstrated using simulated data, and then it was applied to reconstruct both trees from the 2003 H7N7 avian influenza outbreak in the Netherlands.