Evolution requires the generation and optimization of new traits ("adaptation") and involves the selection of mutations that improve cellular function. These mutations were assumed to arise by selection of neutral mutations present at all times in the population. Here we review recent evidence that indicates that deleterious mutations are more frequent in the population than previously recognized and that these mutations play a significant role in protein evolution through continuous positive selection. Positively selected mutations include adaptive mutations, i.e. mutations that directly affect enzymatic function, and compensatory mutations, which suppress the pleiotropic effects of adaptive mutations. Compensatory mutations are by far the most frequent of the two and would allow potentially adaptive but deleterious mutations to persist long enough in the population to be positively selected during episodes of adaptation. Compensatory mutations are, by definition, context-dependent and thus constrain the paths available for evolution. This provides a mechanistic basis for the examples of highly constrained evolutionary landscapes and parallel evolution reported in natural and experimental populations. The present review article describes these recent advances in the field of protein evolution and discusses their implications for understanding the genetic basis of disease and for protein engineering in vitro.