Graphene has been studied extensively in the recent years, especially after it became possible to fabricate it through exfoliation. Its most interesting aspect is the existence of linearly-dispersing gapless excitations in the vicinity of the Dirac points. I will review the history of graphene ``discovery'' as well as recent theoretical and experimental developments in the study of graphene, the open questions and its possible applications in the future. I will then focus on the details of graphene exploration using scanning tunneling microscopy. Graphene has the great advantage that, unlike in most of the other known two-dimensional electron gases, the electrons are confined to the surface, which makes it an ideal candidate for such measurements. I will describe what has been extracted so far from the measurements of the local density of states, and what we can hope to expect in the future from this analysis.