Active systems are assemblies of interacting entities that individually consume energy to generate motion and forces and collectively exhibit organized behaviors on scales much larger than that of the individuals. The active matter paradigm is relevant to phenomena on many scales, from the control of human crowds to the collective migration of epithelial cells in wound healing. We employ theory and computation and make complementary use of bottom-up modeling and top-down phenomenology to investigate the self-organized structural and mechanical properties of these complex systems.