The evolution of phenotypic similarities between species, known as convergence, illustrates that populations can respond predictably to ecological challenges. Convergence often results from similar genetic changes, which can emerge in two ways: the evolution of similar or identical mutations in independent lineages, which is termed parallel evolution; and the evolution in independent lineages of alleles that are shared among populations, which I call collateral genetic evolution. Evidence for parallel and collateral evolution has been found in many taxa, and an emerging hypothesis is that they result from the fact that mutations in some genetic targets minimize pleiotropic effects while simultaneously maximizing adaptation. If this proves correct, then the molecular changes underlying adaptation might be more predictable than has been appreciated previously.