**Abstract:** We study the spectral properties of the two-dimensional Dirac operator on bounded domains together with the appropriate boundary conditions which provide a (continuous) model for graphene nanoribbons. These are of two types, namely the so-called armchair and zigzag boundary conditions, depending on the line along which the material was cut. In the former case, we show that the spectrum behaves in what might be called a ``classical'' way, while in the latter we prove the existence of a sequence of finite multiplicity eigenvalues converging to zero and which correspond to edge states. The results were obtained in collaboration with P. Freitas (GFM, University of Lisbon).