The propagation of a crack across a car's windshield, or the motion of sand under a footstep on the beach, are both everyday examples that highlight the intriguing flow patterns exhibited by disordered materials when subjected to external forcing. Despite their wide prevalence, much is unknown about the physical mechanisms that govern flow in these highly non-linear, out-of-equilibrium systems. In my research, I employ both theory and computer simulations, with the goal of understanding what determines the underlying microscopic structures made by the constituent particles of various materials -- whether they are molecules, grains, fibers or bubbles -- and how these structures affect the way these materials flow.