Assemblies of interacting self-driven entities form soft active materials with intriguing collective behavior and mechanical properties. Examples abound in nature on many scales, from the flocking of birds to cell migration in morphogenesis. They also include synthetic systems, from self-catalytic colloids to autonomously propelled liquid crystals.  What unifies these systems is that they are driven out of equilibrium by dissipative processes that act on each individual particle, hence break the time reversal symmetry of the dynamics at the microscale. This results in surprising behavior. For instance, active fluids flow with no externally applied driving forces, active gases do not fill their container, and active particles spontaneously organize when passive ones would not.  In this talk I will discuss the physics of active matter with examples from both the living and non-living worlds. I will show that by combining minimal physical models with continuum theory and simulations we are making advances towards capturing quantitatively the laws of spontaneous organization of active systems.  This theoretical progress has implication for both formulating design principles for new smart materials and understanding cellular and multicellular organization.