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The present state of knowledge concerning the physical phenomena of high-current interruption with vacuum interrupters (VI) is reviewed. Two arc control methods, application of externally applied axial magnetic field (AMF) or transverse magnetic field (TMF), are available to distribute the heat flux from arc to contacts homogeneously over contact surface, to avoid local overheating. AMF spreads the arc at fixed location. TMF moves the constricted arc over contact surface. Change from diffuse to constricted arcing mode results from superposition of two effects: "instability of anode sheath" and "influence of magneto-gas-dynamic", when no AMF component exists. Conditions of arc memory at current zero determine the process of current extinction and of recovery of breakdown strength to its ultimate value. Evaporation of metal vapor continues. Charge exchange between fast ions and slow vapor atoms increases the residual charge, left in the switching gap at current zero. Post arc current prolongs and increases consequently. Breakdown during recovery of dielectric strength occurs instantaneously or sporadically delayed. Behavior of breakdown is essentially determined by vapor density. Breakdown mechanism of delayed breakdown is still unresolved. Vapor density is too low to initiate breakdown alone. Lack of fundamental knowledge in combination with complexity hampers numerical treatment of arc behavior, as well as heat flux to contact during arcing and process of interruption presently, as needed for interpretation of experimental results and prediction purposes.