Currently, a large number of scientific articles can be found in the research literature in the field focusing on the use of oleogels for food formulation to improve their nutritional properties. The present review focuses on the most representative food-grade oleogels, highlighting current trends in terms of the most suitable methods of analysis and characterization, as well as trends in their application as substitutes for saturated and trans fats in foods. For this purpose, the physicochemical properties, structure, and composition of some oleogelators are primarily discussed, along with the adequacy of oleogel incorporation for use in edible products. Analysis and characterization of oleogels by different methods are important in the formulation of innovative foods, and therefore, this review discusses the most recent published results regarding their microstructure, rheological and textural properties, and oxidative stability. Last but not least, issues related to the sensory properties of oleogel-based foods are discussed, highlighting also the consumer acceptability of some of them.