Graphene has many unique properties that make it an ideal material for fundamental studies as well as for potential applications. Here we review recent results on the Raman spectroscopy and imaging of graphene. We show that Raman spectroscopy and imaging can be used as a quick and unambiguous method to determine the number of graphene layers. The strong Raman signal of single layer graphene compared to graphite is explained by an interference enhancement model. We have also studied the effect of substrates, the top layer deposition, the annealing process, as well as folding (stacking order) on the physical and electronic properties of graphene. Finally, Raman spectroscopy of epitaxial graphene grown on a SiC substrate is presented and strong compressive strain on epitaxial graphene is observed. The results presented here are highly relevant to the application of graphene in nano-electronic devices and help in developing a better understanding of the physical and electronic properties of graphene.