  The nucleon structure functions probed in deep-inelastic scattering at large
virtualities form an important tool to test Quantum Chromdynamics (QCD) through
precision measurements of the strong coupling constant $\alpha_s(M_Z^2)$ and
the different parton distribution functions. The exact knowledge of these
quantities is also of importance for all precision measurements at hadron
colliders. During the last two decades very significant progress has been made
in performing precision calculations. We review the theoretical status reached
for both unpolarized and polarized lepton-hadron scattering based on
perturbative QCD.
