Human fishery product‐borne parasitic diseases are caused by cestodes, trematodes and nematodes and are caused by infection following ingestion of viable parasites, or as allergic (hypersensitivity) reactions against parasite antigens. For allergy, the only parasite in fishery products implicated is the nematode Anisakis simplex, and sensitisation occurs via infection by live larvae. Once sensitised, response to nematode allergens can be highly aggressive and generate severe disease. In a sensitised individual, infection can provoke a concurrent A. simplex allergic episode or can be elicited by exposure to allergen alone from killed parasite: the relative epidemiological impact for each is unknown. Allergy to A. simplex is relatively common in some regions in Spain but rarely reported in other parts of Europe. Prevention of sensitisation is most likely to be effective by control of A. simplex infection. There is more information on the resistance to physical and chemical treatments by A. simplex than for other fishery parasites, and the properties of other parasites are likely to be similar. Many traditional marinating and cold smoking methods are not sufficient to kill A. simplex and freezing or heat treatments remain the most effective processes guaranteeing killing. All wild caught seawater and freshwater fish are must be considered at risk of containing any viable parasites of human health concern if these products are to be eaten raw or almost raw. For wild‐catch fish, no sea fishing grounds can be considered free of A. simplex. For farmed Atlantic salmon reared in floating cages or onshore tanks and fed on compound feedstuffs however, the current risk of infection with anisakids is negligible. Apart from farmed Atlantic salmon, sufficient monitoring data are not available for any other farmed fish therefore it is not possible to identify which fish species do not present a health hazard with respect to the presence of parasites.