I review arguments for the existence of a critical point in the QCD phase
diagram as a function of temperature and baryon chemical potential. I describe
how heavy ion collision experiments at the SPS and RHIC can discover the
tell-tale signatures of such a critical point, thus mapping this region of the
QCD phase diagram. I then review the phenomena expected in cold dense quark
matter: color superconductivity and color-flavor locking. I close with a
snapshot of ongoing explorations of the implications of recent developments in
our understanding of cold dense quark matter for the physics of compact stars.Comment: 29 pages. 4 figures. latex with aipproc. References added and
corrected. One version of this review is to appear in the Comments of Nuclear
and Particle Physics section of Comments on Modern Physics. Other versions
were contributed to the proceedings of the Conference on Intersections of
Nuclear and Particle Physics, Quebec, May 2000 and to the proceedings of the
40th Zakopane School of Theoretical Physics, June 200
