Population genetics is fundamental to our understanding of evolution, and mutations are essential raw materials for evolution. In this introduction to more detailed papers that follow, we aim to provide an oversight of the field. We review current knowledge on mutation rates and their harmful and beneficial effects on fitness and then consider theories that predict the fate of individual mutations or the consequences of mutation accumulation for quantitative traits. Many advances in the past built on models that treat the evolution of mutations at each DNA site independently, neglecting linkage of sites on chromosomes and interactions of effects between sites (epistasis). We review work that addresses these limitations, to predict how mutations interfere with each other. An understanding of the population genetics of mutations of individual loci and of traits affected by many loci helps in addressing many fundamental and applied questions: for example, how do organisms adapt to changing environments, how did sex evolve, which DNA sequences are medically important, why do we age, which genetic processes can generate new species or drive endangered species to extinction, and how should policy on levels of potentially harmful mutagens introduced into the environment by humans be determined?