  QCD at finite density presents specific challenges to lattice gauge theory.
Nonetheless, a region of the QCD phase diagram up to moderately large baryon
chemical potentials has been successfully explored on the lattice and new
results and idea are continuously emerging.
  I will outline the lattice formulation of QCD, introduce the calculational
schemes currently used to treat a nonzero baryon density, and mention lattice
methods alternative to MonteCarlo, including the strong coupling expansion
which might give access to the the superconducting phase of QCD. The results
for the critical line, and the different phases will be discussed highlighting
the strength of the different methods, as well as the possible comparisons with
phenomenological models.
