© 2019 The Authors. Journal of Fish Biology published by John Wiley & Sons Ltd on behalf of The Fisheries Society of the British Isles. Brown trout Salmo trutta is endemic to Europe, western Asia and north-western Africa; it is a prominent member of freshwater and coastal marine fish faunas. The species shows two resident (river-resident, lake-resident) and three main facultative migratory life histories (downstream–upstream within a river system, fluvial–adfluvial potamodromous; to and from a lake, lacustrine–adfluvial (inlet) or allacustrine (outlet) potamodromous; to and from the sea, anadromous). River-residency v. migration is a balance between enhanced feeding and thus growth advantages of migration to a particular habitat v. the costs of potentially greater mortality and energy expenditure. Fluvial–adfluvial migration usually has less feeding improvement, but less mortality risk, than lacustrine–adfluvial or allacustrine and anadromous, but the latter vary among catchments as to which is favoured. Indirect evidence suggests that around 50% of the variability in S. trutta migration v. residency, among individuals within a population, is due to genetic variance. This dichotomous decision can best be explained by the threshold-trait model of quantitative genetics. Thus, an individual's physiological condition (e.g., energy status) as regulated by environmental factors, genes and non-genetic parental effects, acts as the cue. The magnitude of this cue relative to a genetically predetermined individual threshold, governs whether it will migrate or sexually mature as a river-resident. This decision threshold occurs early in life and, if the choice is to migrate, a second threshold probably follows determining the age and timing of migration. Migration destination (mainstem river, lake, or sea) also appears to be genetically programmed. Decisions to migrate and ultimate destination result in a number of subsequent consequential changes such as parr–smolt transformation, sexual maturity and return migration. Strong associations with one or a few genes have been found for most aspects of the migratory syndrome and indirect evidence supports genetic involvement in all parts. Thus, migratory and resident life histories potentially evolve as a result of natural and anthropogenic environmental changes, which alter relative survival and reproduction. Knowledge of genetic determinants of the various components of migration in S. trutta lags substantially behind that of Oncorhynchus mykiss and other salmonines. Identification of genetic markers linked to migration components and especially to the migration–residency decision, is a prerequisite for facilitating detailed empirical studies. In order to predict effectively, through modelling, the effects of environmental changes, quantification of the relative fitness of different migratory traits and of their heritabilities, across a range of environmental conditions, is also urgently required in the face of the increasing pace of such changes.