The studies of the cosmic gamma-ray bursts and soft gamma repeaters that have been performed in the Russian-American Konus-Wind experiment during the last several years have been summarized. The experiment has been continuously performed using the Konus Russian scientific instrument on the Wind American spacecraft since 1994 under the optimal interplanetary space conditions in the absence of noise caused by the Earth’s radiation belts and the shadowing of detectors. Two high-sensitivity detectors have constantly observed the entire celestial sphere and recorded detailed time and spectral characteristics of bursts in a wide range of energies (20 keV–15 MeV). The Konus-Wind data have been widely used in the present-day multiwave studies of gamma-ray bursts.