In contrast to other major forms of livestock agriculture, there is a paucity of scientific information on the welfare of fish raised under intensive aquacultural conditions. This reflects an adherence to the belief that these animals have not evolved the salient biological characteristics that are hypothesised to permit sentience. In this review, we evaluate the scientific evidence for the existence of sentience in fish, and in particular, their ability to experience pain, fear and psychological stress. Teleost fish are considered to have marked differences in some aspects of brain structure and organization as compared to tetrapods, yet they simultaneously demonstrate functional similarities and a level of cognitive development suggestive of sentience. Anatomical, pharmacological and behavioural data suggest that affective states of pain, fear and stress are likely to be experienced by fish in similar ways as in tetrapods. This implies that fish have the capacity to suffer, and that welfare consideration for farmed fish should take these states into account. We suggest that the concept of animal welfare can be applied legitimately to fish. It is therefore appropriate to recognize and study the welfare of farmed fish.