  We review recent results on the coherence and superfluidity of driven
dissipative condensates, i.e., systems of weakly-interacting non-conserved
Bosons, such as polariton condensates. The presence of driving and dissipation
has dramatically different effects depending on dimensionality and anisotropy.
In three dimensions, equilibrium behaviour is recovered at large scales for
static correlations, while the dynamical behaviour is altered by the
microscopic driving. In two dimensions, for an isotropic system, drive and
dissipation destroy the algebraic order that would otherwise exist, however a
sufficiently anisotropic system can still show algebraic phase correlations. We
discuss the consequences of this behaviour for recent experiments measuring
phase coherence, and outline potential measurements that might directly probe
superfluidity.
