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Blazars exhibit the most extreme variability of the class of objects known asactive galactic nuclei (AGN). They are characterized by a featureless continuum, high polarization, and variability at all wavelengths and timescales. The amplitude of optical variations can range from less than 0.1 magnitude on the timescale of minutes to hours, to greater than 5.0 magnitudes on timescales of months to years, and gamma-ray variability amplitudes can span a range of as much as three orders of magnitude in a time-scale as short as a few days. These characteristics are consistent with a supermassive black hole accreting matter at the heart of the host galaxy. However, the observed properties of these objects don't necessarily reflect the intrinsic properties because the emissions have been modified by cosmological distances. The variability of these blazars, which have very different redshifts, have been investigated using several different analytical approaches; i.e. structure function analysis, variability index analysis, and light curve analysis. By transforming observed measurements into the rest frame of the source, the intrinsic properties of the variability can be compared. These variability characteristics of blazars, as seen in their rest frame, and as a function of state, will be discussed in reference to their general characteristics and classification schemes.

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.

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