Studies of the genetic basis of adaptive changes in natural populations are now addressing questions that date back to the beginning of evolutionary biology, such as whether evolution proceeds in a gradual or discontinuous manner, and whether convergent evolution involves convergent genetic changes. Studies that combine quantitative genetics and population genomics provide a powerful tool for identifying genes controlling recent adaptive change. Accumulating evidence shows that single loci, and in some cases single mutations, often have major effects on phenotype. This implies that discontinuous evolution, with rapid changes in phenotype, could occur frequently in natural populations. Furthermore, convergent evolution commonly involves the same genes. This implies a surprising predictability underlying the genetic basis of evolutionary changes. Nonetheless, most studies of recent evolution involve the loss of traits, and we still understand little of the genetic changes needed in the origin of novel traits.