  Artificially engineered light-matter systems constitute a novel, versatile
architecture for the quantum simulation of driven, dissipative phase
transitions and non-equilibrium quantum many-body systems. Here, we review
recent experimental as well as theoretical works on the simulation of
geometrical frustration in interacting photonic systems out of equilibrium. In
particular, we discuss two recent discoveries at the interface of quantum
optics and condensed matter physics: (i) the experimental achievement of
bosonic condensation into a flat energy band and (ii) the theoretical
prediction of crystalline phases of light in a frustrated qubit-cavity array.
We show that this new line of research leads to novel and unique tools for the
experimental investigation of frustrated systems and holds the potential to
create new phases of light and matter with interesting spatial structure.
