The sustainability of future finfish aquaculture needs to be improved to meet global environmental challenges. Global fish aquaculture production has expanded significantly recently, due to the increased demand for fish for human consumption. Therefore, it is important to mitigate challenges to the sustainability of the sector, such as pollution and depletion of natural resources. In this study, we systematically mapped the scientific literature on farm-level sustainability in fish aquaculture. The concept of sustainability was considered holistically, covering its economic, environmental and social dimensions, each consisting of a range of different aspects that may contradict or reinforce each other. Literature published between January 2000 and August 2020 with the geographical focus on Europe, Northern America and Australia–New Zealand was included. The search resulted in a total of 287 hits, but after the exclusion of articles that did not match the scope, only 17 papers remained for the systematic mapping. Of these, five papers covered all three dimensions of sustainability. Economic sustainability was addressed in 10 papers, environmental sustainability in 13 papers and social sustainability in 12 papers. This systematic mapping provides an important foundation for discussions and prioritisations of future actions to increase knowledge on farm-level sustainability in finfish aquaculture.