  Phase transitions, such as the freezing of water and the magnetisation of a
ferromagnet upon lowering the ambient temperature, are familiar physical
phenomena. Interestingly, such a collective change of behaviour at a phase
transition is also of importance to living systems. From cytoplasmic
organisation inside a cell to the collective migration of cell tissue during
organismal development and wound healing, phase transitions have emerged as key
mechanisms underlying many crucial biological processes. However, a living
system is fundamentally different from a thermal system, with driven chemical
reactions (e.g., metabolism) and motility being two hallmarks of its
nonequilibrium nature. In this review, we will discuss how driven chemical
reactions can arrest universal coarsening kinetics expected from thermal phase
separation, and how motility leads to the emergence of a novel universality
class when the rotational symmetry is spontaneously broken in an incompressible
fluid.
