Crop production has become a priority issue in recent years because of the exponential growth of the world’s population and the need to find substitutes for chemical fertilizers. The latter is under the spotlight in order to achieve a more sustainable approach in a cost-effective way. Biostimulants have gained attention as an alternative to chemical fertilizers. Although they are not considered fertilizers as inputs of nutrients, they stimulate plants’ nutrition and tolerance to stress, among other characteristics. In the literature, amino acid-based biostimulants have been found to be effective. This review focuses on the effectiveness of biostimulants, their presence in the global market, and their production with fish by-products as a source, using enzymatic hydrolysis and autolysis, with a particular focus on fish viscera, their possibilities in the agricultural sector, and their availability in Europe for possible opportunities. Fish viscera protein hydrolysates for biostimulant production seem a feasible alternative to fishmeal production in Europe, especially in areas located far from fishmeal plants.