  Active particles may undergo phase separation when interactions oppose
self-propulsion, in the absence of any cohesive forces. The corresponding
Motility-Induced Phase Separation (MIPS) is arguably the simplest non-trivial
collective feature that distinguishes active from passive particles. It is
observed in a large variety of systems which we review in this chapter. We
describe in depth the case of motile particles interacting via quorum-sensing
interactions, whose theoretical framework is by now well-established. We close
the chapter by discussing the features observed in systems undergoing MIPS that
still challenge our understanding.
