In this thesis we present a time-dependent multi-zone radiative transfer code and its applications to study the multiwavelength emission of blazars. The multiwavelength variability of blazars is widely believed to be a direct manifestation of the formation and propagation of relativistic jets, and hence the related physics of the black hole - accretion disk - jet system. However, the understanding of these variability demands highly sophisticated theoretical analysis and numerical simulations. Especially, the inclusion of the light travel time effects(LTTEs) in these calculations has long been realized important, but very difficult. The code we use couples Fokker-Planck and Monte Carlo methods, in a 2 dimensional (cylindrical) geometry. For the first time all the LTTEs are fully considered, along with a proper, full, self-consistent treatment of Compton cooling, which depends on the LTTEs.

Using this code, we studied a set of physical processes that are relevant to the variability of blazars, including electron injection and escape, radiative cooling, and stochastic particle acceleration. Our comparison of the observational data and the simulation results revealed that a combination of all those processes is needed to reproduce the observed behaviors of the emission of blue blazars. The simulation favors that the high energy emission at quiet and flare stages comes from the same location.

We have further modeled red blazars PKS 1510-089. External radiation, which comes from the broad line region (BLR) or infrared torus, is included in the model. The results confirm that external Compton model can adequately describe the emission from red blazars. The emission from BLR is favored as the source of Inverse Compton seed photons, compared to synchrotron and IR torus radiation.