Atlantic salmon (Salmo salar) is one of the best researched fishes, and its aquaculture plays a global role in the blue revolution. However, since the 1970s, tens of millions of farmed salmon have escaped into the wild. We review current knowledge of genetic interactions and identify the unanswered questions. Native salmon populations are typically genetically distinct from each other and potentially locally adapted. Farmed salmon represent a limited number of wild source populations that have been exposed to =12 generations of domestication. Consequently, farmed and wild salmon differ in many traits including molecular-genetic polymorphisms, growth, morphology, life history, behaviour, physiology and gene transcription. Field experiments have demonstrated that the offspring of farmed salmon display lower lifetime fitness in the wild than wild salmon and that following introgression, there is a reduced production of genetically wild salmon and, potentially, of total salmon production. It is a formidable task to estimate introgression of farmed salmon in wild populations where they are not exotic. New methods have revealed introgression in half of ~150 Norwegian populations, with point estimates as high as 47%, and an unweighted average of 6.4% across 109 populations. Outside Norway, introgression remains unquantified, and in all regions, biological changes and the mechanisms driving population-specific impacts remain poorly documented. Nevertheless, existing knowledge shows that the long-term consequences of introgression is expected to lead to changes in life-history traits, reduced population productivity and decreased resilience to future challenges. Only a major reduction in the number of escapees and/or sterility of farmed salmon can eliminate further impacts.