A concise review of the progress of lattice calculations at non-zero density
since QM2006 is given, with emphasis on the high baryon density, low
temperature domain. Possibilities for exploring densities higher than those
studied by standard techniques are analysed. The phase transitions of cold,
dense matter, where the sign problem remains severe, are discussed in the
context of QCD-like models and approximations to QCD.Comment: 8 pages, 8 figures. Plenary talk at Quark Matter 2008: 20th
International Conference on Ultra-Relativistic Nucleus Nucleus Collisions
(QM2008), Jaipur, India, 4-10 Feb 2008. Pdflatex problem fixe