  The k.p method is a semi-empirical approach which allows to extrapolate the
band structure of materials from the knowledge of a restricted set of
parameters evaluated in correspondence of a single point of the reciprocal
space. In the first part of this review article we give a general description
of this method, both in the case of homogeneous crystals (where we consider a
formulation based on the standard perturbation theory, and Kane's approach) and
in the case of non-periodic systems (where, following Luttinger and Kohn, we
describe the single-band and multi-band envelope function method and its
application to heterostructures). The following part of our review is
completely devoted to the application of the k.p method to graphene and
graphene-related materials. Following Ando's approach, we show how the
application of this method to graphene results in a description of its
properties in terms of the Dirac equation. Then we find general expressions for
the probability density and the probability current density in graphene and we
compare this formulation with alternative existing representations. Finally,
applying proper boundary conditions, we extend the treatment to carbon
nanotubes and graphene nanoribbons, recovering their fundamental electronic
properties.
