THE traditional classification of reptiles is based on a single key character, the presence and style of fenestration in the temporal region of the skull. Snakes, lizards, crocodiles, dinosaurs and others are 'diapsids', in that they have (at least primitively) two holes in the temporal region. Reptiles in which the skull is completely roofed, with no temporal fenestration, are the 'anapsids'. These include many Palaeozoic forms such as captorhinomorphs, procolophonids and pareiasaurs, but also include Testudines (turtles and tortoises). Consistent with this assumption, recent analyses of the affinities of Testudines have included Palaeozoic taxa only, placing them as akin to captorhinomorphs1 or procolophonids2 or nested within pareiasaurs3,4. Here we adopt a broader perspective, adding a range of Mesozoic and extant taxa to the analysis. Our result robustly supports the diapsid affinities of turtles, and so requires reassessment of the use of turtles as 'primitive' reptiles in phylogenetic reconstruction. More generally, it illustrates the difficulties of treating groups, such as the Testudines, that have extant members with peculiar morphologies that mask phylogenetic affinity; the hazards of relying on key characters such as temporal fenestration, which may mislead; the problems of outgroup choice for wide-ranging, inclusive analyses that include data from Recent and extinct groups; and the difficulties of judging the value of parsimony when applied to such inclusive analyses.