Seafood contributes a significant proportion of protein to human diet. Due to overfishing, seafood is increasingly supplied by aquaculture. Farmed fish can be affected by a range of diseases, including parasitic diseases, which can have economic impact and cause adverse effects on health of consumers. Risks of outbreaks of parasitic diseases are affected by farming systems. Parasitic infections in aquaculture are particularly common in farming systems with reduced biosecurity, for example, sea cages. As only one commercial vaccine is available against fish parasitic disease and there is a high risk of development of resistance of parasites to medications, selective breeding and other preventative methods are increasingly adopted by aquaculture industry. Current issues and future challenges include improvements in diagnostic methods, co-infections with other parasites and development of novel seafood production systems such as integrated aquaculture, recirculated systems and cellular aquaculture.