This special issue of Systematic Biology contains review articles, contributed by keynote speakers after the fifth edition of the “Mathematical and Computational Evolutionary Biology” conference (MCEB; see web sites below) conference, held in 2013. We started in 2003 (under a slightly different name: “Mathematics of Evolution and Phylogeny”) at the Mathematics Research Center Henri Poincaré, Paris, with well-known speakers like Walter Fitch and Joe Felsenstein. We had the feeling that the considerable efforts of the keynote speakers to synthesize and present their research in an extensive but understanding manner would deserve to be known by a large audience. Two books containing review articles corresponding to keynote presentations were published, following the 2003 and 2005 conference edition (Gascuel 2005; Gascuel and Steel 2007).