Virtually every problem in biology benefits from consideration within an evolutionary frame work. Parasitism has been part of life ever since one organism was able to provide an environment for another: questions of parasitology naturally lend themselves to consideration of the shared ancient history of parasites and hosts. The derivation of that shared history is therefore an area of great interest to theoreticians and practitioners alike. The most intuitive approach to this is by cophylogeny mapping. Mathematically the problem is that of optimally mapping the dependent tree into the independent one, e.g., parasite into host or gene tree into organismal phylogeny. This article describes some of the recent advances in cophylogenetic simulation, significance testing, and theoretical properties of maps. In simulation the author shows that the number of ways of mapping the parasite phylogeny into that of the hosts does indeed grow exponentially quickly in most cases and shows no close correlation with the similarity between the phylogenies, and that under a simple coevolutionary model, the range of behaviours of simulated parasite phylogenies is extremely broad and would appear to confound efforts to infer model parameters from observed cases. In the area of significance testing the author demonstrates that the maximal number of inferred codivergence events is not necessarily the best statistic for measuring cophylogenetic agreement, and that significance testing by randomisation which does not alter the parasite tree substantially biases results, and provides a new test to determine whether phylogenetic similarity is consistent with preferential host switching.