This paper describes comminution processes using the theories of limiting states, elasticity, and plasticity to explain some effects observed in the process of crushing brittle materials. It further describes the phenomena occurring during crushing in high-pressure roll presses and analyzes the effects of selected factors upon crushing results. The evaluation of the usefulness of various hypotheses for interpretation of the crushing process in the high-pressure grinding roll was carried out by means of experimental investigations. A series of laboratory crushing tests were also conducted in which limestone samples were pressed in a hydraulic piston-die press. Comminution conditions in this press are similar to those observed in the working chamber of HPGR presses. The limestone aggregate, placed in a steel cylinder, was exposed to pressure exerted by the stamp of the press. Samples had various particle size distributions, and experiments were conducted for two values of pressing force. Operating pressure was the main parameter influencing the obtained comminution effects, but the particle size distribution also has an impact on the process effects. A comparison of the results of the investigations indicated that there exists a significant potential for adjusting the operational parameters of high-pressure grinding rolls. Internal stresses are a derivate of crushing actions such as compression, impact, bending, and shearing. The result of crushing in a particular crusher depends on the strength properties of particles reacting to a specific type of crushing actions. In every crusher there are many crushing actions out of which one is dominating due to the crusher type. Impact is a dominating factor in impact or hummer crushers. Various actions of crusher elements on the crushed material are beneficiary. For example, the shape of the jaw surface in jaw crushers, cone surface in cone crushers, or roll surface in roll presses are important. [...]