The relationship between genotype (which is inherited) and phenotype (the target of selection) is mediated by environmental inputs on gene expression, trait development, and phenotypic integration. Phenotypic plasticity or epigenetic modification might influence evolution in two general ways: (1) by stimulating evolutionary responses to environmental change via population persistence or by revealing cryptic genetic variation to selection, and (2) through the process of genetic accommodation, whereby natural selection acts to improve the form, regulation, and phenotypic integration of novel phenotypic variants. We provide an overview of models and mechanisms for how such evolutionary influences may be manifested both for plasticity and epigenetic marking. We point to promising avenues of research, identifying systems that can best be used to address the role of plasticity in evolution, as well as the need to apply our expanding knowledge of genetic and epigenetic mechanisms to our understanding of how genetic accommodation occurs in nature. Our review of a wide variety of studies finds widespread evidence for evolution by genetic accommodation. © 2014 The Author(s). Evolution © 2014 The Society for the Study of Evolution.