Since its discovery in less than five years ago, graphene has become one of the hottest frontiers in materials science and condensed matter physics, as evidenced by the exponential increase in number of publications in this field. Several reviews have already been published on this topic, focusing on single and multilayer graphene sheets. Here, we review the recent progresses in this field by extending the scope to various types of two-dimensional carbon nanostructures including graphene and free-standing carbon nanowalls/nanosheets. After a brief overview of the electronic properties of graphene, we focus on the synthesis, characterization and potential applications of these carbon nanostructures.