The method of controlling high-current switching arcs by transverse magnetic fields (TMF) forcing the constricted arc to rotate in a contact system is being applied successfully to improve the breaking capability of vacuum interrupters and gas circuit breakers. We describe the behavior of magnetically driven switching arcs in vacuum and in gas environment. We report on experiments using high-velocity videography, magnetic probes, and spectroscopy; they deliver the velocity, the temperature and the voltage of an arc. We present models and simulations of the moving constricted arc burning in metal vapor and in air. And we describe a particular switching application of TMF arc control and explain a scaling law of the contact size with the current interruption capability.