There is growing interest in replacing meat products with plant-based alternatives for environmental, health, and animal welfare reasons. Plant-based meat analogs are usually designed to have sensorial characteristics that match those of real meat. Lipids play a significant role in this. Therefore, there is interest in using structured plant-based lipids, like oleogels and emulsions, to replace the adipose tissue and other fats in meat analogs. Moreover, there is interest in creating natural antioxidant strategies to improve the quality and shelf life of the lipids in plant-based foods. However, further research is still needed to develop plant-based lipids that accurately mimic the behavior of animal-based ones. This review explores and discusses various technological approaches to address challenges in creating plant-based alternatives to animal fats, particularly in the context of meat and dairy products, to provides insights into innovative approaches for improving the sustainability, health, and sensory attributes of plant-based meat analogs, addressing challenges related to texture, oxidation, and overall product quality.