This brief review focuses on health and biological function as cornerstones of fish welfare. From the function-based point of view, good welfare is reflected in the ability of the animal to cope with infectious and non-infectious stressors, thereby maintaining homeostasis and good health, whereas stressful husbandry conditions and protracted suffering will lead to the loss of the coping ability and, thus, to impaired health. In the first part of the review, the physiological processes through which stressful husbandry conditions modulate health of farmed fish are examined. If fish are subjected to unfavourable husbandry conditions, the resulting disruption of internal homeostasis necessitates energy-demanding physiological adjustments (allostasis/acclimation). The ensuing energy drain leads to trade-offs with other energy-demanding processes such as the functioning of the primary epithelial barriers (gut, skin, gills) and the immune system. Understanding of the relation between husbandry conditions, allostatic responses and fish health provides the basis for the second theme developed in this review, the potential use of biological function and health parameters as operational welfare indicators (OWIs). Advantages of function- and health-related parameters are that they are relatively straightforward to recognize and to measure and are routinely monitored in most aquaculture units, thereby providing feasible tools to assess fish welfare under practical farming conditions. As the efforts to improve fish welfare and environmental sustainability lead to increasingly diverse solutions, in particular integrated production, it is imperative that we have objective OWIs to compare with other production forms, such as high-density aquaculture. However, to receive the necessary acceptance for legislation, more robust scientific backing of the health- and function-related OWIs is urgently needed.