Numerical simulation is a key element in the design of electronic circuits. Huge efforts were devoted to it in the past 30 years allowing to fully benefit from the possibilities provided by circuits and components fabrication technologies. A threshold in the shrinking of components was exceeded these last years. Besides the positive effect on the integration of functions into a single chip and on the elementary power consumption, negative effects appear as electrical parasitic phenomena previously neglected. Simulations are therefore much longer despite the increased performances of computers because elementary components models are more complex and the components count increases. In this report, we present an history of the models and algorithms that are classically used to simulate a circuit at the electrical level. Thereafter, we introduce the so-called non-smooth class of models and algorithms studied at the INRIA, as well as the first results that they yielded in the simulation of simple circuits. The non-smooth approach seems to be a promising solution for the large scale electrical simulation.