Active matter describes systems in which individual units dissipate energy to exert forces on their environment. Abundant in the biological world, active systems can also be engineered in the lab where they take the form of self-propelling droplets, particles and grains. The disconnection between dissipation and injection of energy at the microscopic scale drives these systems strongly out of thermal equilibrium. This leads to a phenomenology markedly different from that of equilibrium systems, such as the emergence of dense phases of matter in the absence of cohesive forces. In this lecture, I will review recent theoretical developments in the study of active-matter systems, from the discovery of their anomalous mechanical properties to the characterization of their rich many-body physics. In particular, I will show how disorder impacts scalar active matter much more strongly than in passive systems.