Bird flocks, living tissues, and colloids propelled by self-catalytic reactions are examples of active matter – collectives of individually driven, dissipative units with fascinating emergent behavior at large scales. Active systems self-organize in complex patterns, with transitions between ordered and disordered states. They are also capable of spontaneously generating forces and sustained motion. Importantly, many aspects of this behavior are described by physical models based on a minimal set of rules or interactions. In this talk I will use examples from the living and nonliving world to highlight common properties of active systems and describe recent progress in capturing their nonequilibrium behavior using theory and simulations.