  We review the theoretical basis and understanding of electronic interactions
in graphene Landau levels, in the limit of strong correlations. This limit
occurs when inter-Landau-level excitations may be omitted because they belong
to a high-energy sector, whereas the low-energy excitations only involve the
same level, such that the kinetic energy (of the Landau level) is an
unimportant constant. Two prominent effects emerge in this limit of strong
electronic correlations: generalised quantum Hall ferromagnetic states that
profit from the approximate four-fold spin-valley degeneracy of graphene's
Landau levels and the fractional quantum Hall effect. Here, we discuss these
effects in the framework of an SU(4)-symmetric theory, in comparison with
available experimental observations.
