The issue of the adverse effects of trans-fatty acids has become more transparent in recent years due to researched evidence of their link with coronary diseases, obesity or type 2 diabetes. Apart from conventional techniques for lipid structuring, novel nonconventional approaches for the same matter, such as enzymatic interesterification, genetic modification, oleogelation or using components from nonlipid origins such as fat replacers have been proposed, leading to a product with a healthier nutritional profile (low in saturated fats, zero trans fats and high in polyunsaturated fats). However, replacing conventional fat with a structured lipid or with a fat mimetic can alternate some of the technological operations or the food quality impeding consumers’ acceptance. In this review, we summarize the research of the different existing methods (including conventional and nonconventional) for tailoring lipids in order to give a concise and critical overview in the field. Specifically, raw materials, methods for their production and the potential of food application, together with the properties of new product formulations, have been discussed. Future perspectives, such as the possibility of bioengineering approaches and the valorization of industrial side streams in the framework of Green Production and Circular Economy in the production of tailored lipids, have been highlighted. Additionally, a schematic diagram classifying conventional and nonconventional techniques is proposed based on the processing steps included in tailored lipid production as a convenient and straightforward tool for research and industry searching for healthy, sustainable and zero trans edible lipid system alternatives.