  A review is given of the QCD corrections to charm quark production in deep
inelastic electron-proton scattering. An outline of the computation of the
virtual photon-parton subprocesses, from which one obtains the heavy quark
coefficient functions, is given. The dominant production mechanisms are
discussed. Further we show that the asymptotic heavy quark coefficient
functions, computed in the limit Q^2 >> m^2, can be derived using the operator
product expansion technique. Further we present the various schemes proposed in
the literature to describe the charm component of the structure function and
compare them with the most recent data from the experiments carried out at
HERA.
