  We review recent progress in the study of the anomalous baryon number
non-conservation at high temperatures and in high energy collisions. Recent
results on high temperature phase transitions are described, and applications
to electroweak baryogenesis are considered. The current status of the problem
of electroweak instanton-like processes at high energies is outlined. This
paper is written on the occasion of Sakharov's 75th anniversary and will appear
in the memorial volume of Uspekhi (Usp. Fiz. Nauk, volume 166, No 5, May 1996).
