Food texture is a major food quality parameter. The physicochemical properties of food changes when processed in households or industries, resulting in modified textures. A better understanding of these properties is important for the sensory and textural characteristics of foods that target consumers of all ages, from children to the elderly, especially when food product development is considered for dysphagia. Texture modifications in foods suitable for dysphagic patients will grow as the numbers of elderly citizens increase. Dysphagia management should ensure that texture-modified (TM) food is nutritious and easy to swallow. This review addresses how texture and rheology can be assessed in the food industry by placing particular emphasis on dysphagia. It also discusses how the structure of TM food depends not only on food ingredients, such as hydrocolloids, emulsifiers, and thickening and gelling agents, but also on the applied processing methods, including microencapsulation, microgels as delivery systems, and 3D printing. In addition, we address how to modify texture for individuals with dysphagia in all age groups, and highlight different strategies to develop appropriate food products for dysphagic patients.