In this chapter, we turn to the phase structure of strongly interacting matter as a function of finite baryon density. We first discuss the different limiting forms for mesonic and baryonic matter, and elaborate the resulting phase pattern. Next, we consider the possible phase structure at low temperature and high baryon density, where deconfinement and chiral symmetry restoration need not coincide. Following this, we survey results obtained on the basis of the Nambu-Jona-Lasinio model, and we conclude with a discussion of the present status of finite density lattice QCD.