Consumers increasingly seek foods that are palatable, healthful, and environmentally friendly. Plant-based yogurts address these consumer preferences, gaining popularity over time. However, plant-based yogurts face challenges with inferior stability and lack the smooth, delicate mouthfeel found in traditional dairy yogurts. Therefore, it is essential to identify the factors influencing the mouthfeel and stability of plant-based yogurts. The review starts with discussing the oral perception processes of semisolid food mouthfeel and the preference of consumers for the mouthfeel of plant-based yogurts. Subsequent sections delve into the impacts of the components of plant-based raw materials, the distinct characteristics of fermentation cultures, and the ramifications of various processing techniques on the texture and mouthfeel of the yogurt. The mouthfeel perception of semisolid foods undergoes a dynamic progression, initially shaped by the food’s rheological attributes and later by its tribological qualities. Factors such as the composition of plant-based ingredients, the incorporation of oils and thickeners, the extracellular polysaccharides (EPS) production capabilities of cultures, and specific heat treatment parameters profoundly influence the gel texture or mouthfeel of plant-based yogurts. Hence, based on the ingredient composition, appropriate additives and processing techniques should be employed to produce plant-based yogurts with an optimal mouthfeel and enhanced stability.