The nutritional quality of processed foods is being increasingly questioned by consumers and the trend toward diets that promote health and well‐being has thus grown significantly. With this in mind, food science has sought to develop products replacing ingredients that can be harmful to consumers. This is not an easy task because, besides health‐ and well‐being‐related issues (e.g., nutritional and eventual nutraceutical properties), the new products must also meet consumers' expectations regarding sensory attributes (e.g., flavor, texture, color), while also complying with the legal regulations of the countries where they are supposed to be sold. These aspects are addressed in this article, with a special focus on the replacement of saturated fats by healthier options. Although saturated fats play an important role in many foods, as a consequence of their technological and organoleptic properties, consumption of saturated fats has been correlated with serious health issues. These factors highlight the need to replace saturated fats with healthier alternatives. One of the options to improve upon these problems is the use of edible structured oils that display a healthier fatty acid profile. As such, the development of oleogels and bigels has been of great interest as a solution for the replacement of saturated fat, and will be explored in‐depth in this review.