  The discovery of the integer quantum Hall effect in the early eighties of the
last century, with highly precise quantization values for the Hall conductance
in multiples of $e^2/h$, has been the first fascinating manifestation of the
topological state of matter driven by magnetic field and disorder, and related
to the formation of non-dissipative current flow. In 2005, several new
phenomena such as the spin Hall effect and the quantum spin Hall effect were
predicted in the presence of strong spin-orbit coupling and vanishing external
magnetic field. More recently, the Zeeman spin Hall effect and the formation of
valley Hall topological currents have been introduced for graphene-based
systems, under time-reversal or inversion symmetry-breaking conditions,
respectively. This review presents a comprehensive coverage of all these Hall
effects in disordered graphene from the perspective of numerical simulations of
quantum transport in two-dimensional bulk systems (by means of the Kubo
formalism) and multiterminal nanostructures (by means of the
Landauer-B\"{u}ttiker scattering and nonequilibrium Green function approaches).
In contrast to usual two-dimensional electron gases, the presence of defects in
graphene generates more complex electronic features such as electron-hole
asymmetry, defect resonances or percolation effect between localized impurity
states, which, together with extra degrees of freedom (sublattice pseudospin,
valley isospin), bring a higher degree of complexity and enlarge the transport
phase diagram.
