The review begins by grouping the fundamental nuclear reactions into two classifications, namely, the usual binary processes and few-particle processes. In the few-particle processes, the possibility of electron-screened cold fusion is remarked. The special features of dense plasmas rest in the enhancement of reaction rates over these fundamental processes due to internuclear many-particle processes. The manyparticle processes arise from a modification of the short-range correlations between reacting nuclei and are the effects related closely to differences between Coulombic chemical potentials before and after the nuclear reactions. Quantum statistical-mechanical formulation of the enhancement factors is presented. Thermodynamic functions for various realizations of dense plasmas, pertinent directly to the reaction-rate theories through the screening properties and free energies, are summarized. Those analyses are then applied to the estimation of nuclear reaction rates in specific examples of dense astrophysical plasmas, namely, the Sun, brown dwarfs, giant planets, white-dwarf progenitors of supernovae, and helium burning on the degenerate stars, as well as in those dense laboratory plasmas that are found in the inertial confinement fusion experiments, in metal hydrides such as PdD and Ti ${\mathrm{D}}_2$, in cluster-impact fusion experiments, and in ultrahigh-pressure liquid metals. The essential similarity between the nuclear fusion reactions in supernovae and those projected in the ultrahigh-pressure liquid metals is particularly emphasized.

DOI:https://doi.org/10.1103/RevModPhys.65.255