Consumers are increasingly interested in decreasing their dietary intake of animal-based food products, due to health, sustainability, and ethical concerns. For this reason, the food industry is creating new products from plant-based ingredients that simulate many of the physicochemical and sensory attributes associated with animal-derived foods, including milk, eggs, and meat. An understanding of how the ingredient type, amount, and organization influence the desirable physicochemical, sensory, and nutritional attributes of these plant-based foods is required to achieve this goal. A potential problem with plant-based diets is that they lack key micronutrients, such as vitamin B12, vitamin D, calcium, and ω-3 fatty acids. The aim of this review is to present the science behind the creation of next-generation nutritionally fortified plant-based milk substitutes. These milk-like products may be formed by mechanically breaking down certain plant materials (including nuts, seeds, and legumes) to produce a dispersion of oil bodies and other colloidal matter in water, or by forming oil-in-water emulsions by homogenizing plant-based oils and emulsifiers with water. A brief overview of the formulation and fabrication of plant-based milks is given. The relationship between the optical properties, rheology, and stability of plant-based milks and their composition and structure is then covered. Approaches to fortify these products with micronutrients that may be missing from a plant-based diet are also highlighted. In conclusion, this article highlights how the knowledge of structural design principles can be used to facilitate the creation of higher quality and more sustainable plant-based food products.