The first goal of this paper was to overview modern approaches to local adaptation, with a focus on the use of population genomics data to detect signals of natural selection in fishes. Several mechanisms are discussed that may enhance the maintenance of genetic variation and evolutionary potential, which have been overlooked and should be considered in future theoretical development and predictive models: the prevalence of soft sweeps, polygenic basis of adaptation, balancing selection and transient polymorphisms, parallel evolution, as well as epigenetic variation. Research on fish population genomics has provided ample evidence for local adaptation at the genome level. Pervasive adaptive evolution, however, seems to almost never involve the fixation of beneficial alleles. Instead, adaptation apparently proceeds most commonly by soft sweeps entailing shifts in frequencies of alleles being shared between differentially adapted populations. One obvious factor contributing to the maintenance of standing genetic variation in the face of selective pressures is that adaptive phenotypic traits are most often highly polygenic, and consequently the response to selection should derive mostly from allelic co-variances among causative loci rather than pronounced allele frequency changes. Balancing selection in its various forms may also play an important role in maintaining adaptive genetic variation and the evolutionary potential of species to cope with environmental change. A large body of literature on fishes also shows that repeated evolution of adaptive phenotypes is a ubiquitous evolutionary phenomenon that seems to occur most often via different genetic solutions, further adding to the potential options of species to cope with a changing environment. Moreover, a paradox is emerging from recent fish studies whereby populations of highly reduced effective population sizes and impoverished genetic diversity can apparently retain their adaptive potential in some circumstances. Although more empirical support is needed, several recent studies suggest that epigenetic variation could account for this apparent paradox. Therefore, epigenetic variation should be fully integrated with considerations pertaining to role of soft sweeps, polygenic and balancing selection, as well as repeated adaptation involving different genetic basis towards improving models predicting the evolutionary potential of species to cope with a changing world.