The flavour of aquatic animal products is distinct from terrestrial foods, facilitating a competitive marketing advantage. However, the flavour of aquatic animals can also be highly variable. Importantly, differences are reported in the flavour of animals from aquaculture and wild‐capture systems. These differences can erode consumer acceptance of aquaculture products and reduce financial returns to producers. Mild ‘fish‐like’, ‘marine’, ‘crustacean‐like’, ‘seafood’ and ‘sweet’ odours are desirable. However, overt ‘fish‐like’, ‘fatty’ and ‘earthy’ odours are quality deficits and cause products to become unpalatable. Odorous volatile compounds are responsible for eliciting these characteristic odours. In this literature review, the odorous volatile compounds of 96 aquatic animal samples are reported, revealing 291 different compounds. Generalist compounds that are integral to the odour of aquatic animals are presented in addition to 86 compounds that elicit key characteristic odours. The influence of these compounds on aquatic animal flavour is explored and the specific factors likely to affect their manipulation in aquaculture products are discussed. The culture environment and diet are critical factors affecting volatile profiles of aquatic animals and are the variables that can be controlled by aquaculture producers. The information presented in this review can underpin the development of innovative aquaculture strategies that prevent environmental exposure of aquatic animals to unpalatable volatile compounds and facilitate the development of aquaculture diets that optimise the volatile profile of edible tissues.