European aquaculture industry should be at the forefront of sustainable development, providing healthy and safe food of the highest quality to the consumer, through an environmentally sound approach. The purpose of this review was to explore in what way the current drive for sustainability has affected what the consumer perceives as quality in fish, specifically in gilthead seabream, one of the most important farmed species in the Mediterranean. It focuses on nutritional aspects such as fish meal and fish oil replacement, quality tailoring through finishing strategies, the influence of different farming systems and the effect of slaughter stress on seabream quality. In general, fish meal and fish oil replacement with vegetable ingredients will result in changes in the fatty acid profile of the fillets, and consequently the potential health benefits seabream offers to the consumer. While organoleptic properties suffer little change, the impact of these ingredients on welfare has not been fully investigated. Further studies are also needed to evaluate the effect of land animal ingredients on seabream quality. In either case, although finishing strategies to restore essential fatty acids are not completely effective, seabream can still retain a high nutritional value. Information on the use of dietary supplements as finishing strategies is still extremely scarce. Regarding fish welfare, the high densities practised in intensive production systems pose concerns which warrant further research in this area. Furthermore, new alternatives for common harvesting and slaughter methods are needed to improve welfare, as traditional methods are clearly stressful.