Recognising faces is widely believed to be achieved using “special” neural and cognitive mechanisms that depend on “holistic” processing, which are not used when recognising other kinds of objects. An important, but largely unaddressed, question is how much like a Human face a stimulus needs to be to engage this “special” mechanism(s). In the current study, we attempted to answer this question in 3 ways. In Experiments 1 and 2 we examined the extent to which the disproportionate inversion effect for human faces extends to the faces of other species (including a range of other primates). Results suggested that the faces of other primates engage the mechanism responsible for the inversion effect approximately as well as that mechanism is engaged by Human faces, but that non-primate faces engage the mechanism less well. And so primate faces, in general, seem to produce a disproportionate inversion effect. In Experiment 3 we examined the extent to which the Composite effect extends to the faces of a range of other primates, and found no compelling evidence of a composite effect for the faces of any other primate. The composite effect was exclusive to Human faces. Because these data differ so dramatically from a previously reported study asking similar questions Taubert (2009), we also (in Experiment 4) ran an exact replication of Taubert’s Experiment 2, which reported on both Inversion and Composite effects in a range of species. We were unable to reproduce the pattern of data reported by Taubert. Overall, the results suggest that the disproportionate inversion effect extends to all of the faces of the non-human primates tested, but that the composite effect is exclusive to Human faces.