The number of farmed fish in the world has increased considerably. Aquaculture is a growing industry that will in the future provide a large portion of fishery products. Moreover, in recent years, the number of teleost fish used as animal models for scientific research in both biomedical and ecological fields has increased. Therefore, it is increasingly important to implement measures designed to enhance the welfare of these animals. Currently, a number of European rules exist as requirements for the establishment, care and accommodation of fish maintained for human purposes. As far as (teleost) fish are concerned, the fact that the number of extant species is much greater than that of all other vertebrates must be considered. Of further importance is that each species has its own specific physical and chemical requirements. These factors make it difficult to provide generalized recommendations or requirements for all fish species. An adequate knowledge is required of the physiology and ecology of each species bred. This paper integrates and discusses, in a single synthesis, the current issues related to fish welfare, considering that teleosts are target species for both aquaculture and experimental models in biological and biomedical research. We first focus on the practical aspects, which must be considered when assessing fish welfare in both research and aquaculture contexts. Next, we address husbandry and the care of fish housed in research laboratories and aquaculture facilities in relation to their physiological and behavioural requirements, as well as in reference to the suggestions provided by European regulations. Finally, to evaluate precisely which parameters described by Directive 2010/63/EU are reported in scientific papers, we analysed 82 articles published by European researchers in 2014 and 2015. This review found that there is a general lack of information related to the optimal environmental conditions that should be provided for the range of species covered by this directive.