  The interplay between different types of disorder and electron-electron
interactions in graphene planes is studied by means of Renormalization Group
techniques. The low temperature properties of the system are determined by
fixed points where the strength of the interactions remains finite, as in one
dimensional Luttinger liquids. These fixed points can be either stable
(attractive), when the disorder is associated to topological defects in the
lattice or to a random mass term, or unstable (repulsive) when the disorder is
induced by impurities outside the graphene planes. In addition, we analyze
mid-gap states which can arise near interfaces or vacancies.
