The principal species of marine aquaculture in Europe are Atlantic salmon (Salmo salar), sea bass (Dicentrarchus labrax) and sea bream (Sparus auratus). For Atlantic salmon and sea bass, a substantial part of total genetic variation is partitioned at the geographical population level. In the case of sea bream, gene flow across the Azores/Mediterranean scale appears to be extensive and population structuring is not detected. For Atlantic salmon and sea bass, natural population structure is at risk from genetic interaction with escaped aquaculture conspecifics. The locally adaptive features of populations are at risk from interbreeding with non-local aquaculture fish. Wild populations, generally, are at risk from interactions with aquaculture fish that have been subject to artificial selection or domestication. Atlantic salmon is the main European aquaculture species and its population genetics and ecology have been well-studied. A general case regarding genetic interactions can be based on the information available for salmon and extended to cover other species, in the appropriate context. A generalized flow chart for interactions is presented. Salmon escape from aquaculture at all life stages, and some survive to breed among wild salmon. Reproductive fitness in the escaped fish is lower than in native, wild fish because of behavioural deficiencies at spawning. However, as the number of salmon in aquaculture greatly exceeds the number of wild fish, even small fractional rates of escape may result in the local presence of large numbers, and high frequencies, of escaped fish. At present, policy and legislation in relation to minimizing genetic interactions between wild and aquaculture fish is best developed for Atlantic salmon, through the recommendations of the Oslo Agreement developed by the North Atlantic Salmon Conservation Organization and subsequent agreements on their implementation. In future, the potential use of genetically modified fish in aquaculture will make additional policy development necessary. Improved containment is recommended as the key to minimizing the numbers and therefore the effects of escaped fish. Emergency recovery procedures are recommended as a back-up measure in the case of containment failure. Reproductive sterility is recommended as a future key to eliminating the genetic potential of escaped fish. The maintenance of robust populations of wild fish is recommended as a key to minimizing the effects of escaped fish on wild populations.