  We review theoretical approaches to explore the phase diagram of nuclear and
quark matter at high baryon density. We first look over the basic properties of
quantum chromodynamics (QCD) and address how to describe various states of QCD
matter. In our discussions on nuclear matter we cover the relativistic
mean-field model, the chiral perturbation theory, and the approximation based
on the large-Nc limit where Nc is the number of colors. We then explain the
liquid-gas phase transition and the inhomogeneous meson condensation in nuclear
matter with emphasis put on the relevance to quark matter. We commence the next
part focused on quark matter with the bootstrap model and the Hagedorn
temperature. Then we turn to properties associated with chiral symmetry and
exposit theoretical descriptions of the chiral phase transition. There emerge
some quark-matter counterparts of phenomena seen in nuclear matter such as the
liquid-gas phase transition and the inhomogeneous structure of the chiral
condensate. The third regime that is being recognized recently is what is
called quarkyonic matter, which has both aspects of nuclear and quark matter.
We closely elucidate the basic idea of quarkyonic matter in the large-Nc limit
and its physics implications. Finally, we discuss some experimental indications
for the QCD phase diagram and close the review with outlooks.
