Fish and algae are the major sources of n-3 polyunsaturated fatty acids (n-3 PUFAs). Globally, there is a rapid increase in demand for n-3 PUFA-rich oils. Conventional oil production processes use high temperature and chemicals, compromising the oil quality and the environment. Hence, alternative green technologies have been investigated for producing oils from aquatic sources. While most of the studies have focused on the oil extraction and enrichment of n-3 PUFAs, less effort has been directed toward green refining of oils from fish and algae. Enzymatic processing and ultrasound-assisted extraction with environment-friendly solvents are the most promising green technologies for extracting fish oil, whereas pressurized extractions are suitable for extracting microalgae oil. Lipase-catalysed ethanolysis of fish and algae oil is a promising green technology for enriching n-3 PUFAs. Green refining technologies such as phospholipase- and membrane-assisted degumming deserve investigation for application in fish and algal oils. In the current review, we critically examined the currently existing research on technologies applied at each of the steps involved in the production of oils rich in n-3 PUFAs from fish and algae species. Special attention was placed on assessment of green technologies in comparison with conventional processing methods.