Active Galactic Nuclei (AGNs) are accreting supermassive black holes at the center of galaxies, known for rich spectral features and multi-time scale variability in their electromagnetic emission. The origin of the variability in AGN light curves can be either intrinsic, meaning related processes that take place inside the AGN system, or extrinsic, i.e., from the propagation of light towards Earth. In this dissertation, I present my work focusing on AGN variability. The first two works focus on the variability of blazars, a subclass of AGN with their relativistic jets beaming towards the observer. The first work combines 3D relativistic magnetohydrodynamics (RMHD) simulations with radiation transfer and shows the kink instability within the blazar jet can cause quasi-periodic radiation signatures within a typical period of time scales from weeks to months. The second work combines 2D Particle-in-Cell (PIC) simulations with radiation transfer and shows that isolated and merging plasmoids due to magnetic reconnection in a blazar environment could produce rich radiation and polarization signatures. The last work explores an extrinsic origin for AGN variability: a scenario in which interstellar medium (ISM) within our galaxy can refract light coming from AGNs. It suggests that plasma structures in ISM with an axisymmetric geometry can account for extreme scattering events (ESEs) in AGN observations. Future research directions include studies of the kink instability in jets that propagate in different environments and simulations of magnetic reconnection in 3D which may reveal additional particle acceleration mechanisms, which may play important role in the resulting radiation and polarization signatures.