Pulsed-power-driven z-pinch plasmas are an intense source of soft X-ray radiation producing, on the Z facility, about 2 MJ of total radiation for a number of tungsten loads and in the case of a multiwire titanium array over 1 MJ total radiation and about 100 kJ from the titanium K-shell. The production and transport of radiation in these non-LTE plasmas are often modeled assuming some variation of Local Thermodynamic Equilibrium (LTE) in conjunction with radiation diffusion. Since these plasmas are neither in LTE or entirely opaque or transparent these models do not properly predict the emitted radiation spectra and yield. Also, application of these models overestimates the radiation cooling to the extent that the evolving hydrodynamic profiles are significantly different from those that would obtain using the appropriate non-LTE model with a more realistic treatment of the radiation transport. In this investigation, we discuss the production and transport of radiation from the viewpoint of the microscopic collisional and radiative processes and then apply it to z-pinch plasmas. Through the use of examples and illustrations, it is shown that for identical initial load conditions, atomic level structure, and rate coefficients, the models predict different results that affect the dynamic evolution and hydrodynamic history of the plasma. As an example, the emission spectrum is generated using a 1-D radiation MHD model self-consistently coupled to a circuit representing the Sandia Z facility. A comparison is then made between several standard models of ionization dynamics for a multiwire titanium array. Finally, we address some of the issues regarding how the dense plasma environment influences isolated atom structure and processes. These include, for example, atomic level shifts, ionization lowering, collision cross sections, and collision widths. Transition from the isolated-atom to the dressed-particle picture can modify the ionization physics and emission spectra to such an extent that it may challenge our precepts on how best to design loads for the next generation machine.