Quantum simulations in phase-space: from quantum optics to ultra-cold physics

As a contribution to the international year of light, we give a brief history of quantum optics in phase-space, with new directions including quantum simulations of multipartite Bell violations, opto-mechanics, ultra-cold atomic systems, matter-wave Bell violations, coherent transport and quantum fluctuations in the early Universe. We mostly focus on exact methods using the positive- P representation, and semiclassical truncated Wigner approximations. (invited comment)