Theoretical study of QCD phase diagram at High Baryon Density

Searching for signals of phase transitions in dense QCD is one of the most important but challenging subjects in relativistic heavy-ion collisions. Mediums with various densities and temperatures can be produced in these experiments with the variation of the collision energy, and they are ongoing worldwide at RHIC-STAR, GSI-HADES, NA61/SHINE, etc. In this talk, I would like to discuss several theoretical topics concerning the search for the QCD critical point and a color-superconducting phase transition in these experiments. These topics include the search for the QCD critical point with non-Gaussian fluctuations and the use of the ultra-low-energy region of the dilepton production rate as a signal of the second-order phase transition in dense QCD. The present status of the J-PARC heavy ion program, which is a future experiment that investigates dense quark matter, will also be reviewed.