  We review the theoretical and experimental results connected with the
electron states in two-dimensional Dirac systems paying a special attention to
the atomic collapse in graphene. Two-electron bound states of a Coulomb
impurity are considered too. A rather subtle role of a magnetic field in the
supercritical charge problem in graphene is discussed. The electron states in
the field of two equally charged impurities are studied and the conditions for
supercritical instability to occur are determined. It is shown that the
supercriticality of novel type is realized in gapped graphene with two unlikely
charged impurities. For sufficiently large charges of impurities, it is found
that the wave function of the occupied electron bound state of the highest
energy changes its localization from the negatively charged impurity to the
positively charged one as the distance between the impurities increases. The
specifics of the atomic collapse in bilayer graphene is considered and it is
shown that the atomic collapse in this material is not related to the
phenomenon of the fall-to-center.
