The experimental data on the initiation of a number of nuclear processes in a plasma produced by an ultrashort laser pulse of intensity 1016—1021 W cm-2 are summarised. These processes include excitation of nuclear levels, fusion and fission reactions, production of unstable isotopes, generation of ultrashort pulses of elementary particles, etc. The trends and outlook for studies aimed at increasing the intensity, energy, and average power of ultrashort laser pulses are analysed.