Fish are the main source of long-chain polyunsaturated fatty acids (LC-PUFA, >C18) for human consumption. In general, it has been widely observed that the fatty acid (FA) profiles of farmed fish are reflective of the diet. However, the degree of tissue FA “distortion” based on incorporation of different dietary FA into fish tissues varies greatly depending on FA type, fish species and environmental factors. In terms of fish FA composition, this variation has not been comprehensively reviewed, raising the question: “Are fish what they eat?”. To date, this remains unanswered in detail. To this end, the present review quantitatively summarized the ‘diet-fish’ FA relationship via an analysis of FA composition in diets and fish tissues from 290 articles published between 1998 and 2018. Comparison of this relationship among different fish species, tissue types or individual FA was summarized. Furthermore, the influence of environmental factors such as temperature and salinity, as well as of experimental conditions such as fish size and trophic level, feeding duration, and dietary lipid level on this relationship are discussed herein. Moreover, as a means of restoring LC-PUFA in fish, an emphasis was paid to the fish oil finishing strategy after long-term feeding with alternative lipid sources. It is envisaged that the present review will be beneficial in providing a more comprehensive understanding of the fundamental relationship between the FA composition in diets, and subsequently, in the farmed fish. Such information is integral to maintaining the quality of farmed fish fillets from the perspective of FA composition. •The ‘diet-fish’ FA relationship was systematically reviewed.•The ‘diet-fish’ FA relationship was analyzed by quantitative approaches.•Factors influencing the ‘diet-fish’ FA relationship were analyzed and discussed.•An emphasis was paid to the fish oil finishing strategy in fish farming.•Dietary FA incorporation in fish tissues is affected by many non-dietary factors.