  These notes are based on lectures given during the Summer School `Active
matter and non-equilibrium statistical physics', held in Les Houches in
September 2018. In these notes, we have merged our lectures into a single
chapter broadly dedicated to `Non-equilibrium active systems'. We start with a
discussion of generic features of non-equilibrium statistical mechanics,
followed by a description of selected examples of the possible consequences of
not being at thermal equilibrium. We then introduce the topic of dense glassy
materials with a short review of glassy dynamics, rheology and jamming
transitions for systems that are not active. We then discuss dense active
materials, from simple mean-field theories to numerical models and experimental
realizations. Finally, we discuss two examples of materials driven out of
equilibrium by an oscillatory driving force.
