The farming of salmon and other marine finfish in open net pens continues to increase along the world's coastlines as the aquaculture industry expands to meet human demand. Farm fish are known to escape from pens in all salmon aquaculture areas. Their escape into the wild can result in interbreeding and competition with wild salmon and can facilitate the spread of pathogens, thereby placing more pressure on already dwindling wild populations. Here we assess the ecological, genetic, and socioeconomic impacts of farm salmon escapes, using a risk-assessment framework. We show that risks of damage to wild salmon populations, ecosystems, and society are large when salmon are farmed in their native range, when large numbers of salmon are farmed relative to the size of wild populations, and when exotic pathogens are introduced. We then evaluate the policy and management options for reducing risks and discuss the implications for farming other types of marine finfish.