About 10% of all galaxies are active, meaning their nuclear region is brighter than the rest of the galaxy's emission combined. A subset of active galactic nuclei are more than 100 time brighter than the galactic emission and produce bipolar jets as the accretion disk and supermassive black hole interact. Blazars occur when one jet is pointed toward Earth, and represent the most energetic sustained phenomena in the known Universe. As such, blazars provide us with an unparalleled view of the extreme physics occurring in jets near compact objects, like black holes. I utilize first-principles physical concepts to create theoretical models of the primary emitting region of blazar jets, which help us to understand the physical properties behind broadband spectral emission and time variability signatures from these astrophysical powerhouses.

Blazars are luminous extragalactic sources across the entire electromagnetic spectrum, but the spectral formation mechanisms in these sources are not well understood. We develop a series of self-consistent theoretical models for the emitting region in a blazar jet with one zone, leptonic transport equations. Our transport models consider shock acceleration, adiabatic expansion, stochastic acceleration due to MHD waves, Bohm diffusive particle escape, synchrotron radiation, and Compton radiation. We solved the steady-state and time-dependent Thomson regime transport equations analytically, and produced predictions for the X-ray spectrum and X-ray time lags of Mrk 421. We developed a physical picture in which a subset of the electrons is disproportionately accelerated by the presence of a shock.

Furthermore, we implement the full Compton cross-section for electron interactions with photons from dust and 26 lines from the stratified broad line region, each considered individually. We use the solution for the electron distribution to calculate multi-wavelength SED spectra for 3C 279. This new, self-consistent model provides an unprecedented view into the jet physics at play in this source, especially the relative strength of the shock and stochastic acceleration components and the size and location of the emitting region. We show that our blazar model is the first to successfully fit the Fermi-LAT gamma-ray data for this source based on a first-principles physical calculation. We also provide physical insight into the acceleration mechanisms that dominate blazar emission on different timescales.