I spell out and update the individuality thesis, that species are individuals, and not classes, sets, or kinds. I offer three complementary presentations of this thesis. First, as a way of resolving an inconsistent triad about natural kinds; second, as a phylogenetic systematics theoretical perspective; and, finally, as a novel recursive account of an evolved character. These approaches do different sorts of work, serving different interests. Presenting them together produces a taxonomy of the debates over the thesis, and isolates ways (...) it has been productive. This goes to the larger point of this paper: a defense of the individuality thesis in terms of its utility, and an update of it in light of recent theoretical developments and empirical work in biology. (shrink)