Résumé : In this chapter, the numerical time integration methods for switched electronic circuits are described with a focus on the event--capturing time--stepping schemes based on the complementarity theory. After briefly introducing the strengths and weaknesses of various simulation approaches (hybrid, regularised and nonsmooth), the mathematical nature of solutions for dynamical complementarity systems are discussed in view of numerical time--integration. Then the formulation of the time–stepping methods via complementarity will be described. For each class of solutions, a suitable method is provided and its properties will be illustrated on simple electrical circuits. Some implementation details will be then explained. Especially, the complementarity solvers that are used at each time–step will be described recalling the main families of available solvers. Some insights on the software implementation will also be given. Finally, numerical applications and examples on more realistic circuits will be considered. We will mainly focus on the architecture of a power converter : the Buck converter.