Recently developed sub‐picosecond pulse lasers have been used to create hot, near solid density plasmas. Since these plasmas are nearly in local thermodynamic equilibrium (LTE), their emission spectra involve a huge number of populated configuration. A typical spectrum is a combination of many unresolved clusters of emission, each containing an immense number of overlapping, unresolvable bound‐bound and bound‐free transitions. Under LTE, or near LTE conditions, traditional detailed configuration or detailed term spectroscopic models are not capable of handling the vast number of transitions involved. The average atom (AA) model, on the other hand, accounts for all relevant transitions, but in an oversimplified fashion that ignores all spectral structure. The Super Transition Array (STA) model, which we have developed in recent years, combines the simplicity and comprehensiveness of the AA model with the accuracy of detailed term accounting. The resolvable structure of spectral clusters is revealed by successively increasing the number of distinct STA’s, until convergence is attained. The limit of this procedure is a detailed unresolved transition array (UTA) spectrum, with a term‐broadened line for each accessible configuration‐to‐configuration transition, weighted by the relevant Boltzman population.In practice, we have found that this UTA spectrum is actually obtained using only a few thousand to tens of thousands of STA’s (as opposed, typically, to billions of UTAs). The central result of STA theory is a set of formulas for the moments (total intensity, average transition energy, variance) of an STA. In calculating the moments, we use detailed relativistic first order quantum transition energies and probabilities. The energy appearing in the Boltzman factor associated with each level in a superconfiguration is the zero order result corrected by a superconfiguration averaged first order correction. As the number of configurations in a superconfiguration is successively decreased, this becomes equivalent to using exact first order configuration average energies. In addition, orbital relaxation can be accounted for by recalculating orbitals and energies for each STA in a potential optimized for the particular set of configurations. Examples and application to recent measurements are presented.