Calculations of thermodynamic and radiative characteristics of hot dense plasmas within different quantum-statistical approaches, such as the use of the Hartree–Fock–Slater model and the ion model, are presented. Calculated equations of state of different substances are used to investigate findings from absolute and relative measurements of the compressibility of solid aluminum samples in strong shock waves. It is shown that our calculated Hugoniot adiabat of aluminum is in a good agreement with experimental data and other theoretical results from first principles. We also present a review of the most important applications of the quantum-statistical approach to the study of radiative properties of hot dense plasmas. It includes the optimization problem of hohlraum wall materials for laser inertial fusion, calculations of the radiative efficiency of complex materials for optically thin plasma in X-pinch, modeling of radiative and gas-dynamic processes in plasma for experiments, where both intense laser and heavy ion beams are used, and temperature diagnostics for X- and Z-pinch plasmas.