Multipactor is a resonant vacuum discharge occurring in microwave components of satellite systems as well as in particle accelerators. Due to its undesirable effects, multipactor analysis constitutes a mandatory step in the design of modern satellite components and in performance studies of particle accelerators. To this end, the development of computational techniques for multipactor prediction attracts intense interest in the scientific community. The phenomenon evolves in two distinct phases: first, a fast growth of the electron population and, second, a steady state during which the population reaches a saturation level and remains almost constant. State-of-the-art computational models focus on the precise prediction of the initial multipactor phase, which defines whether the discharge occurs or not. However, a clear overview of the phenomenon also requires the analysis of the longterm multipactor evolution. Due to the high complexity introduced by considering saturation mechanisms, long-term multipactor evolution remains still unclear for many configurations of highly practical importance. Such a case is the multipactor analysis in the presence of dielectrics, a case dealt within this thesis. Motivated by the challenging nature of analyzing the multipactor steady state, this work aims to provide its own contribution to the modeling and the analysis of long-term multipactor evolution. For this, a sophisticated computational tool has been developed for the full-3D multipactor analysis, taking into account saturation mechanisms. In order to get a fast overview of the phenomenon, a generalized single-electron model has been developed which allows a multipactor analysis in any configuration with unidirectionallike electric field. Based on this 1D model, qualitative studies considering the effect of lowenergy electron collisions and of single-sided multipactor in non-uniform coaxial fields have been performed. As a further step, a multiple-particle, full-3D model able to consider the stochastic nature of the secondary emission phenomenon has been developed. The singleelectron model nicely supplements the robust 3D analysis by providing fast estimations for the most likely cases in which multipactor occurs. Saturation mechanisms have been considered, too, for both 1D and 3D approximations. Taking into account the induced charges on the metallic boundaries, a fast analysis of longterm multipactor is provided by the 1D model for the parallel plate and coaxial line cases. The saturation study is boosted in the 3D analysis by taking into account the mutual Coulomb interaction between particles. The developed multipactor model has been properly adapted in order to study long-term multipactor in the case of dielectric-loaded waveguides. Space charge effects as well as the effect of the surface charge developed on the dielectric layer have been both considered in the analysis. Particularly, in order to efficiently take into account the effect of the induced charges, a novel image method for the evaluation of the 3D Green function in multi-layered media has been developed. For the first time, a saturation steady state is identified in parallel plates loaded with a dielectric layer.