Air Cherenkov methods in cosmic rays: Review and some history

Radiation first discovered by Pavel Cherenkov is used for developing a variety of methods in cosmic-ray studies. Among them, air Cherenkov methods form a separate area with several lines of research. Numerous applications of air Cherenkov radiation in studies of extensive air showers, in γγ-astronomy and neutrino physics are reviewed. A tribute is given to Alexander Chudakov whose pioneer ideas and experimental skill laid foundation for the present-day progress.