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 one 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. This paper is focused on the theoretical challenges raised by the atomic modeling of dense, non-ideal plasmas. It is intended to give a synthetic and pedagogical view on the evolution of ideas in the field, with an accent on the theoretical consistency issues, rather than an exhaustive review of models and experimental benchmarks. 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.