Codes and data files for the figures displayed in "Markov genealogy processes", (Theoretical Population Biology 143: 77-91, 2022, doi: 10.1016/j.tpb.2021.11.003). See also the arXiv preprint. Abstract: We construct a family of genealogy-valued Markov processes that are induced by a continuous-time Markov population process. We derive exact expressions for the likelihood of a given genealogy conditional on the history of the underlying population process. These lead to a nonlinear filtering equation which can be used to design efficient Monte Carlo inference algorithms. We demonstrate these calculations with several examples. Existing full-information approaches for phylodynamic inference are special cases of the theory.