Electroweak baryon number non-conservation in the early Universe and in high-energy collisions

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.