  The edges of graphene and graphene like systems can host localized states
with evanescent wave function with properties radically different from those of
the Dirac electrons in bulk. This happens in a variety of situations, that are
reviewed here. First, zigzag edges host a set of localized non dispersive state
at the Dirac energy. At half filling, it is expected that these states are
prone to ferromagnetic instability, causing a very interesting type of edge
ferromagnetism. Second, graphene under the influence of external perturbations
can host a variety of topological insulating phases, including the conventional
Quantum Hall effect, the Quantum Anomalous Hall (QAH) and the Quantum Spin Hall
phase, in all of which phases conduction can only take place through
topologically protected edge states. Here we provide an unified vision of the
properties of all these edge states, examined under the light of the same one
orbital tight-binding model. We consider the combined action of interactions,
spin orbit coupling and magnetic field, which produces a wealth of different
physical phenomena. We briefly address what has been actually observed
experimentally.

Mesoscale and Nanoscale Physics