Selective breeding is an effective tool to improve livestock. Several selection experiments have been conducted to study direct selection responses as well as correlated responses in traits of skeletal muscle growth and function. Moreover, comparisons of domestic with wild-type species and of extreme breeds provide information on the genetic background of the skeletal muscle phenotype. Structural muscular components that differed with increasing distance in lean growth or meat quality in mammals were found to be myofibre number, myofibre size, proportions of fibre types as well as the numbers and proportions of secondary and primary fibres. Furthermore, markers of satellite cell proliferation, metabolic enzyme activities, glycogen and fat contents, the expression of myosin heavy chain isoforms, of activated AMPKα and other proteins in skeletal muscle tissue and circulating IGF1 and IGF-binding proteins have been identified to be involved in selection responses observed in pigs, cattle and/or chicken. The use of molecular methods for selective breeding of fish has only recently been adopted in aquaculture and studies of the genetic basis of growth and flesh quality traits are scarce. Some of the molecular markers of muscle structure/metabolism in livestock have also been identified in fish, but so far no studies have linked them with selection response. Genome scans have been applied to identify genomic regions exhibiting quantitative trait loci that control traits of interest, for example, muscle structure and meat quality in pigs and growth rate in chicken. As another approach, polymorphisms in candidate genes reveal the relationship between genetic variation and target traits. Thus, in large-scale studies with pigs’ associations of polymorphisms in the HMGA2, CA3, EPOR, NME1 and TTN genes with traits of carcass and meat quality were detected. Other studies revealed the significance of mutations in the IGF2 and RYR1 genes for carcass lean and muscle fibre traits in pigs. Mutations in the myostatin (MSTN) gene in fish were also examined. Advances in research of the genetic and environmental control of traits related to meat quality and growth have been made by the application of holistic ‘omics’ techniques that studied the whole muscle-specific genome, transcriptome and proteome in relation to muscle and meat traits, the development of new methods for muscle fibre typing and the adaptation of biophysical measures to develop parameters of muscle fibre traits as well as the application of in vitro studies. Finally, future research priorities in the field are defined.