What might be called well-behaved simple C*-algebras are now, over sixty years after Glimm, classified by means of a simple invariant---in the stable case, the two K-groups (even and odd) together with the tracial cone paired with the even K-group. The groups are arbitrary countable abelian groups, the cone an arbitrary metrizable compactly based lattice cone, and the pairing arbitrary. "Well-behaved" means separable and amenable, and absorbing tensorially the Jiang-Su C*-algebra (also, obeying the UCT, possibly redundant). Recently, Chun Guang Li, Zhuang Niu, and I have shown that the unital simple C*-algebras of stable rank one constructed by Villadsen, not classifiable as above, can nevertheless be classified, for a fixed mildly restricted seed space (the basic input in the Villadsen construction), by the simple invariant consisting of, as expected, the multiplicity information in the even K-group (an arbitrary dense subgroup of the group of rational numbers containing the integers---alternatively, a supernatural number---just, as pointed out by Dixmier, the invariant of Glimm for UHF algebras), together with nothing but a single strictly positive real number, the Toms-Blackadar radius of comparison (based on an ostensibly more sophisticated invariant, the Cuntz semigroup). (The tracial simplex is irrelevant---it is the Poulsen simplex. Conceivably the seed space also doesn't matter---if one keeps track of the K-groups of the simple algebra.)