The assessment of welfare in aquatic animals is currently under debate, especially concerning those kept by humans. The classic concept of animal welfare includes three elements: The emotional state of the organism (including the absence of negative experiences), the possibility of expressing normal behaviors, and the proper functioning of the organism. While methods for evaluating their emotions (such as fear, pain, and anguish) are currently being developed for aquatic species and understanding the natural behavior of all aquatic taxa that interact with humans is a task that requires more time, the evaluation of internal responses in the organisms can be carried out using analytical tools. This review aims to show the potential of the physiology of crustaceans, cephalopods, elasmobranchs, teleosts, and dipnoans to serve as indicators of their wellbeing. Since the classical methods of assessing welfare are laborious and time-consuming by evaluation of fear, pain, and anguish, the assessment may be complemented by physiological approaches. This involves the study of stress responses, including the release of hormones and their effects. Therefore, physiology may be of help in improving animal welfare.