There is growing interest in the design and fabrication of next-generation plant-based (NG-PB) foods that have physicochemical and functional properties that simulate those of traditional animal-based foods, like meat, seafood, egg, and dairy products. Many of these products can be considered as colloidal materials containing particles or polymers that determine their properties, which means that these properties can be understood using soft matter physics concepts. The rheological properties of NG-PB foods may vary widely, including low viscosity fluids (like milk), high viscosity fluids (creams), soft solids (like yogurt), and hard solids (like some cheeses). For manufacturers of NG-PB foods to mimic this broad range of products it is important to have theoretical models to identify, predict, and control the key parameters impacting their textural attributes. In this article, the theoretical models developed to describe the properties of fluid, semi-solid, and solid colloidal dispersions are described, and their potential for improving the design and fabrication of NG-PB foods is highlighted. In the future, it will be important to establish the most appropriate models for different categories of NG-PB foods and to determine their range of applications.