Phenetic classification corresponds to no biological model and lacks a sound philosophical basis. Cladistics (ignoring meaningless “transformed cladistics”) assumes divergent evolution and, usually, that best estimates of phylogeny are obtained by parsimony principles, both questionable assumptions at times. It is better than phenetics since more-or-less testable hypotheses are generated, but pitfalls are many, in data selection and interpretation (as to homology), and in commensurability of units and direction of change. Above all we learn: homoplasy is rife in nature. Much bad cladistics has been done. If it is to reflect phylogeny, classification cannot be artificially stabilized, but is its only aim to express (hypothesized) cladistic patterns? And can it do that with any degree of overall assurance? Biologists are legitimately interested in defining grades as well as clades. Recognition of an unequivocal clade-grade frequently leaves a paraphyletic grade residue that cannot itself be unequivocally resolved. This is a real problem that requires attention in formal taxonomy and in applying cladistics. Primarily morphological cladistics will be increasingly supplanted by molecular (nucleotide-sequence) cladistics. The role of evolutionary taxonomy will change accordingly.