Understanding the nuclear matter equation of state (EOS) is a central goal of 
nuclear physics that cuts across a variety of disciplines. 
Indeed, the limits of nuclear existence, the structure of neutron stars, and 
the dynamics of core-collapse supernova, all depend critically on the nuclear matter EOS. 
In this talk I will concentrate on the EOS of cold baryonic matter with special emphasis 
on its impact on the structure and dynamics of neutron stars. 
In particular, I will discuss the many fascinating phases that are encountered as one 
travels from the low-density crust to the high-density core.