Electrical transport studies on graphene have been focused mainly on the linear dispersion region around the Fermi level(1,2) and, in particular, on the effects associated with the quasiparticles in graphene behaving as relativistic particles known as Dirac fermions(3-5). However, some theoretical work has suggested that several features of electron transport in graphene are better described by conventional semiconductor physics(6,7). Here we use scanning photocurrent microscopy to explore the impact of electrical contacts and sheet edges on charge transport through graphene devices. The photocurrent distribution reveals the presence of potential steps that act as transport barriers at the metal contacts. Modulations in the electrical potential within the graphene sheets are also observed. Moreover, we find that the transition from the p- to n-type regime induced by electrostatic gating does not occur homogeneously within the sheets. Instead, at low carrier densities we observe the formation of p-type conducting edges surrounding a central n-type channel.