  The properties of matter at finite baryon densities play an important role
for the astrophysics of compact stars as well as for heavy ion collisions or
the description of nuclear matter. Because of the sign problem of the quark
determinant, lattice QCD cannot be simulated by standard Monte Carlo at finite
baryon densities. I review alternative attempts to treat dense QCD with an
effective lattice theory derived by analytic strong coupling and hopping
expansions, which close to the continuum is valid for heavy quarks only, but
shows all qualitative features of nuclear physics emerging from QCD. In
particular, the nuclear liquid gas transition and an equation of state for
baryons can be calculated directly from QCD. A second effective theory based on
strong coupling methods permits studies of the phase diagram in the chiral
limit on coarse lattices.
