A few grams of any material contain a bewildering number of individual particles. Interactions between these particles give rise to a vast array of emergent phenomena which cannot be understood from looking at any of the particles in isolation. An important example of this is superconductivity, which enables materials to conduct electricity without resistance. Novel emergent states also occur out of equilibrium, due to the presence of large external forces or the occurrence of extreme events. Examples include turbulence in fluids and plasmas, the spreading of epidemics and diseases, and shocks in the stock market. The above examples illustrate the breadth of this nationally and internationally recognised "Grand Challenge" in Emergence and Physics Far From Equilibrium. Addressing this Grand Challenge requires a coordinated approach, spanning different areas of physics and related disciplines. The Network will facilitate cross-cutting workshops and advanced working groups to enable UK researchers to plan and carry out targeted research programmes. Pump-prime initiatives and interaction with industry will stimulate collaborative research, ensuring UK competitiveness in this far-reaching field.