Analysis of an extensive new molecular dataset for the moss class Polytrichopsida provides convincing support for many traditionally recognised genera and identifies higher level phylogenetic structure with a strong geographic component. A large apical clade that is most diverse in the northern hemisphere is subtended by a grade of southern temperate and tropical genera, while the earliest diverging lineages have widely separated relictual distributions. However, there is strongly supported topological incongruence between the nuclear 18S rRNA gene tree and the chloroplast and mitochondrial data for the positions of some taxa and notably for the status of Pogonatum. While Pogonatum is unambiguously paraphyletic in the 18S tree, it is well supported as monophyletic by the combined chloroplast and mitochondrial data, this being corroborated by several distinctive morphological synapomorphies and a 51-53 bp deletion in the rps4-trnS spacer. We explore various reticulate historical processes and methodological issues as possible explanations for incongruence, and suggest that either (1) the 18S topology is an artefact created by convergence of substitutions at specific sites due to functional and/or molecular-structural constraints not accounted for by the model, or (2) the incongruence is a product of ancient hybridization events. Under the latter scenario, incongruent topologies for Pogonatum are parsimoniously explained if Polytrichum (including Polytrichastrum sect. Aporotheca) is ultimately descended from a hybridization event involving an extinct maternal taxon derived from the branch ancestral to the combined Pogonatum/Polytrichum s.l. clade, and a paternal taxon belonging to (or ancestral to) the apical Pogonatum group to which the majority of extant species belong. Numerous novel relationships of taxonomic and evolutionary significance are supported. Notably, both Polytrichastrum and Oligotrichum are polyphyletic. While Polytrichastrum sect. Aporotheca is closely related to Polytrichum, other species, including the type, are not. The large majority of Oligotrichum species sampled occur in one of two distantly related clades with predominantly northern and southern hemisphere distributions, respectively, implying convergent evolution of this morphology in each of the two temperate zones.