In the present day, it has been widely established that a high intake of animal fat that contains a high content of saturated fatty acids may cause several life-threatening diseases, including obesity, diabetes-type 2, cardiovascular diseases, as well as several types of cancer. In this context, a great number of health organizations and government agencies have launched campaigns to reduce the saturated fat content in foods, which has prompted the food industry, which is no stranger to this problem, to start working to develop foods with a lower fat content or with a different fatty acid profile. Nevertheless, this is not an easy task due to the fact that saturated fat plays a very important role in food processing and in the sensorial perception of foods. Actually, the best way to replace saturated fat is with the use of structured vegetable or marine oils. The main strategies for structuring oils include pre-emulsification, microencapsulation, the development of gelled emulsions, and the development of oleogels. This review will examine the current literature on the different (i) healthier oils and (ii) strategies that will be potentially used by the food industry to reduce or replace the fat content in several food products.