Abstract: In an active galactic nucleus (AGN), the central region of a galaxy is brighter than the rest of the galaxy and sometimes -10,000 times as bright as an average galaxy. The extremely high luminosities of AGNs are thought to be produced by the accretion of matter onto a supermassive black hole (1 million-10 billion solar masses). In many cases AGNs produce two oppositely directed jets of magnetized plasma moving at near-light speed that are luminous over a large range of wavelengths. Understanding the structure and ongoing physical processes of AGNs has important implications in cosmology, galaxy formation theory, black hole physics and other areas of astronomical interest. Due to their large distances, AGNs are not spatially resolved with current and near-future technologies except by radio interferometry. However, we can use time variability, one of the defining properties of AGNs, to probe the location and physical processes related to the emission at resolutions even finer than provided by very long baseline interferometry (VLBI). This dissertation employs extensive multi-frequency monitoring data of the blazar 3C 279 (over >10 years) and the radio galaxies 3C 120 and 3C 111 (>5 years) at X-ray, optical, and radio wavebands, as well as monthly VLBI images. The study develops and applies a set of statistical tools to characterize the time variability of AGNs, including power spectral density (PSD), discrete cross-correlation functions and calculation of their significance. This involves generation of light curves simulated randomly from the previously calculated PSDs. Numerical models of the time variable emission spectrum of the jets and accretion disk-corona system relate the variability to the physics and locations of the various emission regions of the AGN. The analysis leads to the inferences that (1) multiple nonthermal emission zones occur in the jet, (2) acceleration of the highest energy electrons in the jet is often gradual, (3) optical emission from the radio galaxies arises mainly in the accretion disk, and (4) the X-ray emitting hot electrons above the disk lie within about 50 gravitational radii from the black hole.