Conventional phylogenetic analysis for characterizing the relatedness between taxa typically assumes that a single relationship exists between species at every site along the genome. This assumption fails to take into account recombination which is a fundamental process for generating diversity and can lead to spurious results. Recombination induces a localized phylogenetic structure which may vary along the genome. Here, we generalize a hidden Markov model (HMM) to infer changes in phylogeny along multiple sequence alignments while accounting for rate heterogeneity, the hidden states refer to the unobserved phylogenic topology underlying the relatedness at a genomic location. The dimensionality of the number of hidden states (topologies) and their structure are random (not known a priori) and are sampled using Markov chain Monte Carlo algorithms. The HMM structure allows us to analytically integrate out over all possible changepoints in topologies as well as all the unknown branch lengths.