The role of mutations have been subject to many controversies since the formation of the Modern Synthesis of evolution in the early 1940ties. Geneticists in the early half of the twentieth century tended to view mutations as a limiting factor in evolutionary change. In contrast, natural selection was largely viewed as a “sieve” whose main role was to sort out the unfit but which could not create anything novel alone. This view gradually changed with the development of mathematical population genetics theory, increased appreciation of standing genetic variation and the discovery of more complex forms of selection, including balancing selection. Short-term evolutionary responses to selection are mainly influenced by standing genetic variation, and are predictable to some degree using information about the genetic variance–covariance matrix (G) and the strength and form of selection (e. g. the vector of selection gradients, β). However, predicting long-term evolution is more challenging, and requires information about the nature and supply of novel mutations, summarized by the mutational variance–covariance matrix (M). Recently, there has been increased attention to the role of mutations in general and M in particular. Some evolutionary biologists argue that evolution is largely mutation-driven and claim that mutation bias frequently results in mutation-biased adaptation. Strong similarities between G and M have also raised questions about the non-randomness of mutations. Moreover, novel mutations are typically not isotropic in their phenotypic effects and mutational pleiotropy is common. Here I discuss the evolutionary origin and consequences of mutational pleiotropy and how multivariate selection directly shapes G and indirectly M through changed epistatic relationships. I illustrate these ideas by reviewing recent literature and models about correlational selection, evolution of G and M, sexual selection and the fitness consequences of sexual antagonism.