Rates of pycnonuclear reactions in ultradense fluids and solids are evaluat
ed by taking account of recent progress in quantum-statistical formulations
of the equations of state and phase transitions in dense matter. New theor
etical results are summarized for the reaction rates and the enhancement fa
ctors, obtained through systematic studies of the screening effects by rela
tivistic and nonrelativistic electrons, as well as of the thermodynamic pro
perties of dense matter resulting from internuclear cohesion in electron-sc
reened Coulombic fluids and solids; the results prove to be a significant i
mprovement over those in a previous review [S. Ichimaru, Rev. Mod. Phys. 65
, 255 (1993)]. On the basis of these theoretical developments, coupled with
renovated experiments in ultrahigh-pressure metal physics, outstanding iss
ues of nuclear reactions in stellar and planetary interiors and in terrestr
ial settings are explored, with inertial-confinement-fusion experiments, an
d for a novel scheme of fusion studies in dense liquid-metallic proton-deut
eron mixtures. (C) 1999 American Institute of Physics. [S1070-664X(99)01807
-8].