Consumers are interested in plant-based alternatives (PBAs) to dairy and meat products, and as such, the food industry is responding by developing a variety of different plant-based food items. For these products to be successful, their textural properties must be acceptable to consumers. These textural properties need to be thoroughly investigated using different sensory methodologies to ensure consumer satisfaction. This review paper aims to summarize the various textural properties of PBAs, as well as to discuss the sensory methodologies that can be used in future studies of PBAs. PBAs to meat have been formulated using a variety of production technologies, but these products still have textural properties that differ from animal-based products. Most dairy and meat alternatives attempt to mimic their conventional counterparts, yet sensory trials rarely compare the PBAs to their meat or dairy counterparts. While most studies rely on consumers to investigate the acceptability of their products’ textural properties, future studies should include dynamic sensory methodologies, and attribute diagnostics questions to help product developers characterize the key sensory properties of their products. Studies should also indicate whether the product is meant to mimic a conventional product and should define the target consumer segment (ex. flexitarian, vegan) for the product. The importance of textural properties to PBAs is repeatedly mentioned in the literature and thus should be thoroughly investigated using robust sensory methodologies.