  Modeling plasmas in terms of atoms or ions is theoretically appealing for
several reasons. When it is relevant, the notion of atom or ion in a plasma
provides us with an interpretation scheme of the plasma's internal functioning.
From the standpoint of quantitative estimation of plasma properties, atomic
models of plasma allow to extend many theoretical tools of atomic physics to
plasmas. This notably includes the statistical approaches to the detailed
accounting for excited states, or the collisional-radiative modeling of
non-equilibrium plasmas, which is based on the notion of atomic processes. In
this paper, we focus on the challenges raised by the atomic modeling of dense,
non-ideal plasmas.
  First we make a brief, non-exhaustive review of atomic models of plasmas,
from ideal plasmas to strongly-coupled and pressure-ionized plasmas. We discuss
the limitations of these models and pinpoint some open problems in the field of
atomic modeling of plasmas.
  We then address the peculiarities of atomic processes in dense plasmas and
point out some specific issues relative to the calculation of their
cross-sections. In particular, we discuss the modeling of fluctuations, the
accounting for channel mixing and collective phenomena in the photoabsorption,
or the impact of pressure ionization on collisional processes.
