Graphite has been widely used by humans for a large part of their history. Nevertheless, it has only recently been possible to isolate its basic unit: carbon atoms arranged in a honeycomb structure on a single plane, namely graphene. Since its discovery, many techniques have been developed and improved to properly synthesize graphene and its derivatives which are part of the novel class of two-dimensional materials. These advanced materials have imposed themselves in nanotechnology thanks to some outstanding physical properties due to their reduced dimensions. In the case of graphene, its reduced dimension gives rise to a high electrical mobility, a large thermal conductivity, a high mechanical resistance, and a large optical transparency. Therefore, such aspect is of great scientific interest for both basic and applied research, ranging from theoretical physics to surface chemistry and applied solid state physics. The connection between all these fields is guaranteed by spectroscopy and especially by Raman spectroscopy which provides a lot of information about structural and electronic features of graphene. In this review, the authors present a systematized collection of the most important physical insights on the fundamental electronic and vibrational properties of graphene, their connection with basic optical and Raman spectroscopy, and a brief overview of main synthesis methods.