  Phase-space representations are of increasing importance as a viable and
successful means to study exponentially complex quantum many-body systems from
first principles. This review traces the background of these methods, starting
from the early work of Wigner, Glauber and Sudarshan. We focus on modern
phase-space approaches using non-classical phase-space representations. These
lead to the Gaussian representation, which unifies bosonic and fermionic
phase-space. Examples treated include quantum solitons in optical fibers,
colliding Bose-Einstein condensates, and strongly correlated fermions on
lattices.
