Texture analysis is a well-established analytical technique in the food industry for evaluating the mechanical and physical characteristics of both raw ingredients and finished products. Instrumental mechanical properties of table grapes, acquired using universal testing machines equipped with specific probes, may be of interest in the viticulture and postharvest sectors to recognize the potential of each variety and help satisfy market requirements. The measured parameters are related to some sensory properties and, therefore, indirectly to consumer acceptability of the product. As texture analysis is a rapid and low-cost analytical technique, it can also be favorably applied in enology as a routine tool for monitoring winegrape quality. Among the different mechanical parameters measurable, berry skin thickness and hardness are indices that reflect anthocyanin extractability and dehydration kinetics with adequate reliability. This review collects the most recent research results from grape texture studies, emphasizes the potentiality and limits of this analytical technique when applied to grape studies, and highlights trends that require further understanding.