Fruits are not isotropic materials and their structure plays a key role in the control of physical and transport properties, bioavailability of some nutrients, texture perception, appearance, flavor, and other quality attributes. Therefore, preserving the structure is a major objective of the postharvest processing of fruits, as changes in structure lead to detrimental changes in texture, flavor, appearance, and mechanical and nutritional properties. The material properties of fruit tissues are difficult to predict and to explain because of the complex connections and multivariate interdependencies of the structural elements and their changes with time and/or processing, and the biological material variability and heterogeneity. This chapter intends to integrate microscopic structure studies, rheological analysis, and texture perception to have a better understanding of the structure-rheological property relationship and its impact on the texture of minimally processed fruits. After a brief consideration of the structure and heterogeneity of fruits and common tests to evaluate rheological properties, some examples exploring how changes in the structure of fruit tissues subjected to different minimal processes are expressed in rheological parameters are described.