In this talk I discuss the emergence of novel universal critical behaviour in one-dimensional driven open quantum Bose gases in the presence of diffusive Markovian noise.  Salient features are the persistence of both non-equilibrium conditions as well as quantum coherence close to the critical point. This provides a non-equilibrium analogue of quantum criticality, sharply distinct from more generic driven systems where both effective thermalisation as well as asymptotic decoherence ensue, paralleling classical dynamical criticality. The novel critical point is characterised by the full set of independent critical exponents, which are extracted from a functional renormalisation group suited for the Keldysh action.