Graphene is a truly two-dimensional (2D) material with exceptional electronic, mechanical, and optical properties. As such, it consists of surface only and can be probed by the welldeveloped surface science techniques such as, e.g., scanning tunneling microscopy (STM). This method bridges the gap between the surface science community and the electronic device community and might lead to novel combined approaches. Here, I review some of the STM and scanning tunneling spectroscopy (STS) experiments on monolayer graphene samples. I will concentrate on graphene samples deposited on insulating substrates, since these are related to graphene device concepts. In particular, I will discuss the morphology of graphene on SiO 2 and other emerging substrates, some nanomechanical manipulation experiments using STM, and spectroscopic results. The latter can map the disorder potentials as well as the interaction of the electrons with the disorder, which is most pronounced in the quantum Hall regime.Three-dimensional representation of a STM image of graphene; the atomic resolution is displayed as color code, while the rippling is shown in three dimensions (courtesy of M. Pratzer, RWTH Aachen).