Consumption of animal fats, calorie-dense and simple carbohydrate-rich diets along with a more sedentary life style have triggered the outcome of cardiovascular and obesity disorders. A worthy alternative is to replace these of saturated fats with healthier ingredients in a texturized oleogel. Oleogelation promises to decrease the incorporation of harmful fats granting good mechanical properties to food products by creating crystalline colloidal networks upon contact with a gelator. Thus, unsaturated fatty acids from oils are thus trapped and retained forming gels having microscopic self-assembled crystalline particles of different shapes. Currently, most oleogels have been developed with vegetable oils by applying gelators such as polymers, partial glycerides, waxes and fatty acids improving the mechanical and thermal properties of food products. This review is focused on the progress regarding oleogelation and the physical interactions responsible for the intermolecular conformation, physical properties, additives and microstructure required for the substitution of harmful saturated and trans fats. Likewise, the most recent advances, regarding their potential functionality and applications as the fats of the future are also discussed.