- We report two experiments on graphene nanostructures. The first was performed on a graphene nanoribbon, where the nature of electronic transport was investigated in detail. Electrons or holes are found to localize in pockets of the potential along the ribbon. Transport is governed by the joint action of localization and Coulomb interaction. The temperature-dependence of the conductance shows activated behavior at temperatures above a few Kelvin. The activation energy retraces the edges of Coulomb blockade diamonds found in nonlinear transport. In the second experiment the metallic tip of a low- temperature scanning force microscope was scanned above a graphene quantum dot. In addition to the familiar Coulomb blockade fringes, localized states are detected forming in the constrictions connecting the dot to source and drain.