In this paper, we present the operation principles of high current circuit-breakers, the technological problems and the corresponding basic phenomena. For SF6 high-voltage circuit breaker (HVCB) where current interruption occurs near current zero (AC current) the main problems are related to the breakdown due to the recovery voltage and the presence of PTFE vapours. We emphasise the problems studied during the arc decay and the post-arc phase, showing the ability of 2D models including turbulence effects, to predict the plasma cooling and power interruption of the apparatus. For LVCB, the arc created by contact separation is moved by hydrodynamic and magnetic forces, to an extinguishing chamber splitting the arc. The main problems are the displacement of the arc, plasma and gas flow, interaction with the walls and with the splitters, risk of restriking near the contacts and deposition of powders within the apparatus. We will present some models showing the 3-D movement of the plasma and the gas in the circuit-breaker chamber or able to predict the arc velocity in reasonable agreement with diagnostics results.