The interaction between the flutes of counter-rotating rolls and the geometrical features and mechanical properties of the wheat kernel formed the basis for the roller milling revolution leading to the modern flour milling process, in which wheats of varying hardness can be effectively fractionated into bran and high yields of relatively pure white flour. The initial breakage of the wheat creates a particle size distribution that dictates the flows through the rest of the flour milling process and hence the qualities and yields of the resulting flour streams. This breakage depends on the roll gap and disposition and on the size and hardness of the wheat kernels, resulting in particles that vary not only in size but also in composition, with larger particles containing more bran, small particles more endosperm. Recent work on the effects of debranning on breakage, modelled using the breakage equation, and on extending the breakage to include composition, has yielded new insights about the physical mechanisms operating during roller milling of wheat. Roller milling creates large flat bran particles from which endosperm material is scraped through the differential action of the rolls, dependent on roll gap and disposition. Debranning precludes the creation of large flat bran particles, hence compromising this scraping action, resulting in less production of small endosperm material and greater production of mid-range particles. Meanwhile, compositional analysis and modelling using a compositional breakage equation helps to clarify the origin of particles in terms of botanical tissues (outer pericarp, aleurone layer and starchy endosperm).