  In this article we review the quantum Hall physics of graphene based
two-dimensional electron systems, with a special focus on recent experimental
and theoretical developments. We explain why graphene and bilayer graphene can
be viewed respectively as J=1 and J=2 chiral two-dimensional electron gases
(C2DEGs), and why this property frames their quantum Hall physics. The current
status of experimental and theoretical work on the role of electron-electron
interactions is reviewed at length with an emphasis on unresolved issues in the
field, including assessing the role of disorder in current experimental
results. Special attention is given to the interesting low magnetic field limit
and to the relationship between quantum Hall effects and the spontaneous
anomalous Hall effects that might occur in bilayer graphene systems in the
absence of a magnetic field.
