Traditional animal welfare paradigms have focused on maintaining physical health and mitigating negative impacts to wellbeing. Recently, however, the field has increasingly recognized the importance of positive welfare (i.e., mental and physical states that exceed what is necessary for immediate survival) and accordingly introduced manipulations and indicators of positive welfare for use in agriculture, laboratories, and zoos/aquaria. The creation and monitoring of positive welfare requires an in-depth knowledge of species-specific behavior and biology, which necessitates species-specific or, at a minimum, taxa-specific standards. Research on positive welfare in fish is lagging in this regard and therefore merits further consideration. In this paper, we aim to merge what is already known about positive welfare with the existing fish behavior literature to develop a plan of action for fish welfare research that will ultimately contribute to the development of positive welfare standards and assessment strategies for fish. We begin by exploring the origins of positive welfare research and then outline the physical, psychological and species-specific areas of inquiry that can be investigated in fish. In addition to presenting current findings on fish motivation, emotion, potential sources of positive welfare such as fulfillment of motivational urges (establishing agency, engaging in exploration and learning), and play behavior, we also identify promising areas for future research aimed at developing accurate and appropriate indicators of positive welfare in fish.