Atomic physics of dense plasmas is a fascinating, complex and often difficult topic in plasma physics that draws from many scientific disciplines and is an integral part of the description of high energy-density plasmas, magnetic fusion plasmas, laser-plasma interactions and the science of warm condensed matter. In this talk, characteristic "equilibrium" states will be reviewed, including local thermodynamic equilibrium (LTE), Near-LTE, Coronal, line-supported, nebular and Collisional-Radiative equilibrium. The surrounding plasma modifies atomic structure through the Stark effect, continuum lowering, and pressure ionization. Recent experiments showing evidence for these phenomena will be surveyed. The talk will address the challenging search for a better basic formulation that leads to unified and consistent pictures for the equation of state, conductivity and X-ray opacity. Special emphasis is placed on the development of practical models efficient enough for everyday use in advanced simulation codes and yet containing the most important physical processes."