Accretion disks around black holes emit across the electromagnetic spectrum, providing a window into strong-field gravity and extreme plasma environments. By analyzing their light curves and spectra, astrophysicists aim to probe fundamental questions about relativistic dynamics and high-energy astrophysics. Traditionally, models of black hole accretion have assumed that the disk's angular momentum is aligned with the black hole's spin axis. However, both observations and theoretical considerations increasingly suggest that misalignment—or tilt—is common. In this talk, I will present new insights from cutting-edge radiative general relativistic magnetohydrodynamic (GRMHD) simulations of tilted accretion disks. These simulations reveal that radiative cooling can induce a dramatic nonlinear response: disk warping leads to tearing, breaking the flow into discrete, misaligned sub-disks. The resulting dynamics naturally drive disk precession, which may underlie the quasi-periodic oscillations frequently observed in X-ray binaries and active galactic nuclei. In the second part of the talk, I will question the prevailing view that accretion is primarily driven by magnetorotational instability (MRI)-induced turbulence. I will show that in tilted, warped disks, accretion can instead be mediated by large-scale hydrodynamic shocks—specifically, nozzle shocks—offering a possible explanation for rapid luminosity variability in certain active galactic nuclei.