Increasing demand for eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) containing fish oils is putting pressure on fish species and numbers. Fisheries provide fish for human consumption, supplement production and fish feeds and are currently supplying fish at a maximum historical rate, suggesting mass-scale fishing is no longer sustainable. However, the health properties of EPA and DHA long-chain (LC) omega-3 polyunsaturated fatty acids (PUFA) demonstrate the necessity for these oils in our diets. EPA and DHA from fish oils show favourable effects in inflammatory bowel disease, some cancers and cardiovascular complications. The high prevalence of these diseases worldwide indicates the requirement for alternative sources of LC-PUFA. Strategies have included plant-based fish diets, although this may compromise the health benefits associated with fish oils. Alternatively, stearidonic acid, the product of α-linolenic acid desaturation, may act as an EPA-enhancing fatty acid. Additionally, algae oils may be a promising omega-3 PUFA source for the future. Algae are beneficial for multiple industries, offering a source of biodiesel and livestock feeds. However, further research is required to develop efficient and sustainable LC-PUFA production from algae. This paper summarises the recent research for developing prospective substitutes for omega-3 PUFA and the current limitations that are faced.