The connections between geometric structures on a surface S and representations of its fundamental group Gamma have been well-documented. For instance, Teichmuller space, the space of marked hyperbolic structures on S, also has an algebraic description in terms of homomorphisms of into PSL(2,R). Representations into other Lie groups G correspond to other types of geometric structures, so the structure of representation varieties Hom(Gamma,G)/G has been the subject of much study. We will introduce the motivating examples and describe some of the recent research in this area, and exploit the connection between surface groups and right-angled Artin groups to give new, explicit constructions of faithful, discrete representations of surface groups into higher-rank Lie groups.