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, many of which will be presented at this meeting.

Here I will outline the lattice formulation of QCD, introduce the calculational schemes currently used to treat a nonzero baryon density -- the different reweighting techniques, the Taylor expansion from zero chemical potential, the analytic continuation from an imaginary chemical potential -- and mention possible lattice methods alternative to MonteCarlo, including the strong coupling expansion which might give access to the superconducting/CFL phase of QCD. A recurrent theme of this talk will be the interplay of phenomenological models and lattice results, particularly concerning the test of the numerical methods, the analysis of the critical line and the study of the properties of the plasma phase.