The Atlantic bluefin tuna (Thunnus thynnus) is one of the tunas with the highest commercial value and it is supporting the capture-based tuna aquaculture industry in the Mediterranean Sea. This is a seasonal activity and it involves the capture of fish from the wild and their rearing in sea cages for periods ranging between 3 months to 2 years. Short-term rearing is done mainly to: (a) achieve a greater body fat percentage and (b) obtain a better price by not flooding the market in the brief fishing period. Due to the increasing fear of a collapse of the fishery, the International Commission for the Conservation of Atlantic Tunas currently reduced the total allowable catches for 2010 to 13,500 mtn from 32,000 mtn previously. Therefore, there is great interest in establishing a proper and sustainable tuna aquaculture industry. This necessitates the development of specific technologies for tuna aquaculture that will not rely on captured individuals from the wild, as it is practiced today. This article reviews the methods used for the farming and fattening of the species in the Mediterranean Sea, and the current status of the efforts at controlling reproduction in captivity.