This paper studies the electronic states of graphene nanoribbons with zigzag and armchair edges. The electronic properties of narrow graphene ribbons are strongly influenced by their width and geometry. The finite width of these systems breaks the spectrum into an infinite set of bands, which can be understood using the Dirac equation with appropriate boundary conditions. For zigzag nanoribbons, the boundary condition allows for particle- and hole-like bands with evanescent wavefunctions confined to the surfaces, which become zero energy surface states as the width increases. For armchair edges, the boundary condition leads to admixing of valley states, and the band structure is metallic when the width is a multiple of 3 lattice constants, and insulating otherwise. Tight-binding calculations and solutions of the Dirac equation agree quantitatively for all but the narrowest ribbons. Zigzag nanoribbons support surface states that approach zero energy as the ribbon width increases. These states exist only within a specific range of wavevectors between the Dirac points. Armchair nanoribbons do not have surface states, but they can have zero energy states for certain widths, leading to oscillating behavior between insulating and metallic states as the width changes. The continuum description of graphene is shown to be useful for quantitative analysis of these systems, except for the most narrow ones. The results are compared with tight-binding calculations, showing good agreement for all but the narrowest ribbons. The study highlights the importance of boundary conditions in determining the electronic properties of graphene nanoribbons.This paper studies the electronic states of graphene nanoribbons with zigzag and armchair edges. The electronic properties of narrow graphene ribbons are strongly influenced by their width and geometry. The finite width of these systems breaks the spectrum into an infinite set of bands, which can be understood using the Dirac equation with appropriate boundary conditions. For zigzag nanoribbons, the boundary condition allows for particle- and hole-like bands with evanescent wavefunctions confined to the surfaces, which become zero energy surface states as the width increases. For armchair edges, the boundary condition leads to admixing of valley states, and the band structure is metallic when the width is a multiple of 3 lattice constants, and insulating otherwise. Tight-binding calculations and solutions of the Dirac equation agree quantitatively for all but the narrowest ribbons. Zigzag nanoribbons support surface states that approach zero energy as the ribbon width increases. These states exist only within a specific range of wavevectors between the Dirac points. Armchair nanoribbons do not have surface states, but they can have zero energy states for certain widths, leading to oscillating behavior between insulating and metallic states as the width changes. The continuum description of graphene is shown to be useful for quantitative analysis of these systems, except for the most narrow ones. The results are compared with tight-binding calculations, showing good agreement for all but the narrowest ribbons. The study highlights the importance of boundary conditions in determining the electronic properties of graphene nanoribbons.