Appears in collection : 2025 IHES Summer School – Statistical Aspects of Nonlinear Physics

Active materials are driven out of equilibrium at the microscopic scale, where individual units dissipate energy stored in the environment to inject momentum into the system. These energetic and mechanical drives out of thermal equilibrium endow active systems which a rich phenomenology, unmatched in passive systems. In this series of lectures, I will review standard models of active particles and discuss their modeling and collective behaviors. I will show how approximate theories and exact methods combine to shed light on a variety of collective phenomena encountered in active systems, focusing in particular on motility-induced phase separation and the transition to collective motion.