Recent work of Fock-Goncharov and Garoufalidis-D.Thurston-Zickert allows to study representations of fundamental groups of 2- or 3-dimensional manifolds via parameters attached to a triangulation of the manifold. We will outline this combinatorial approach and we will present applications to the investigation of surface group representations in SL(3,R) (joint work in progress with Sungwoon Kim and Jaejeong Lee) and of 3-manifold group representations in SL(4,R).