We probe the local inhomogeneities of the electronic properties of graphene at the nanoscale using scanning probe microscopy techniques. First, we focus on the study of the electronic inhomogeneities caused by the graphene-substrate interaction in graphene samples exfoliated on silicon oxide. We find that charged impurities, present in the graphene-substrate interface, perturb the carrier density significantly and alter the electronic properties of graphene. This finding helps to understand the observed device-to-device variation typically observed in graphene-based electronic devices. Second, we probe the effect of chemical modification in the electronic properties of graphene, grown by chemical vapour deposition on nickel. We find that both the chemisorption of hydrogen and the physisorption of porphyrin molecules strongly depress the conductance at low bias indicating the opening of a bandgap in graphene, paving the way towards the chemical engineering of the electronic properties of graphene.