Resumen: A high consumption of solid fats is linked to increased inflammation and a risk of cardiovascular diseases. Hence, in recent years, there has been increasing interest in the development of oleogels as a fat substitute in food products. Oleogels are edible gels that contain a large amount of liquid oils entrapped in a 3D network and that can potentially be applied to spreads, bakery goods, meat, and dairy products in order to lower their saturated fat content while maintaining a desirable food texture and mouthfeel. In this work, alginate cryogels were studied as templates for three different edible oils in the process of oleogel formation. Two different freezing regimes to obtain cryogels were employed in order to evaluate better the textural and morphological capabilities of cryogels to adsorb and retain edible oils. It was shown that rapid freezing in liquid nitrogen produces alginate cryogels with a lower density, higher porosity, and a greater ability to adsorb the tested oils. The highest uptake and holding oil capacity was achieved for olive oil, which reached a value of 792% and 82%, respectively. The best chewiness was found for an oleogel containing olive oil, whereas oleogels with the other two tested oils showed better springiness. Hence, the results presented in this work demonstrated that alginate-based cryogels can be effectively used as templates for oleogels and potentially find applications in the food industry.