The agricultural world today is dominated by a few domesticated mammal species, that is, animals modified from their wild ancestors through selective breeding in captivity for traits beneficial to human usages. As a result, a clear dichotomy exists between wild (from hunting) and domesticated mammals (produced in farms) used for human consumption. Similar to agriculture, aquaculture is often viewed as the only solution that can provide more fish products given that harvesting wild stocks have reached an upper limit. Aquaculture is considerably younger than agriculture relying on natural sources to farm numerous species. To better describe the diverse strategies for fish production, we propose a new classification comprising five levels of `domestication' with 1 being the least to 5 being the most domesticated. Our classification places 70% of the 250 farmed finfish species recorded in the 2009 FAO database into levels 1, 2 and 3 representing a transitory form of fish production dependent on the availability of the wild resource. In contrast, only a few species, or more accurately populations, can be considered truly domesticated, similar to cattle or sheep. Based on this classification, two scenarios for the future of aquaculture are discussed: either the industry focuses on few truly domesticated species, similar to the path taken by agriculture, but avoiding its negative impacts or aquaculture proceeds with inter-specific diversification by focusing primarily on the domestication of native species.