Reconstructing evolutionary relationships using Bayesian inference has become increasingly popular due to the ability of Bayesian inference to handle complex models of evolution. In this review we concentrate on inference of recombination events between strains of viruses when these events are sporadic, ie rare relative to point mutations. Bayesian inference is especially attractive in the detection of recombination events because it allows for simultaneous inferences about the presence, number and location of crossover points and the identification of parental sequences. Current frequentist recombination identification falls into a sequential testing trap. The most likely parental sequences and crossover points are identified using the data and then the certainty of recombination is assessed conditional on this identification. After briefly outlining basic phylogenetic models, Bayesian inference and Markov chain Monte Carlo (MCMC) computation, we summarise three different approaches to recombination detection and discuss current challenges in applying Bayesian phylogenetic inference of recombination.