  Epistasis occurs when the effect of a mutation depends on its carrier's
genetic background. Despite increasing evidence that epistasis for fitness is
common, its role during evolution is contentious. Fitness landscapes, mappings
of genotype or phenotype to fitness, capture the full extent and complexity of
epistasis. Fitness landscape theory has shown how epistasis affects the course
and the outcome of evolution. Moreover, by measuring the competitive fitness of
sets of tens to thousands of connected genotypes, empirical fitness landscapes
have shown that epistasis is frequent and depends on the fitness measure, the
choice of mutations for the landscape, and the environment in which it was
measured. Here, I review fitness landscape theory and experiments and their
implications for the role of epistasis in adaptation. I discuss theoretical
expectations in the light of empirical fitness landscapes and highlight open
challenges and future directions towards integrating theory and data, and
incorporating ecological factors.
