We give an overview of the coherence properties of exciton-polariton condensates generated by optical parametric scattering. Different aspects of the first-order coherence (g((1))) have been investigated. The spatial coherence extension of a two-dimensional (2D) polariton system, below and at the parametric threshold, demonstrates the development of a constant phase coherence over the entire condensate, once the condensate phase transition takes place. The effect on coherence of the photonic versus excitonic nature of the condensates is also examined. The coherence of a quasi-1D trap, composed of a line defect, is studied, showing the detrimental effect of reduced dimensionality on the establishment of the long range order. In addition, the temporal coherence decay, g((1))(tau), reveals a fast decay in contrast with the 2D case. The situation of a quasi-1D condensate coexisting with a 2D one is also presented.