  There is a broad consensus that accretion onto supermassive black holes and
consequent jet formation power the observed emission from active galactic
nuclei (AGNs). However, there has been less agreement about how jets form in
accretion flows, their possible relationship to black hole spin, and how they
interact with the surrounding medium. There have also been theoretical concerns
about instabilities in standard accretion disk models and lingering
discrepancies with observational constraints. Despite seemingly successful
applications to X-ray binaries, the standard accretion disk model faces a
growing list of observational constraints that challenge its application to
AGNs. Theoretical exploration of these questions has become increasingly
reliant on numerical simulations owing to the dynamic nature of these flows and
the complex interplay between hydrodynamics, magnetic fields, radiation
transfer, and curved spacetime. We conclude the following: The advent of
general relativistic magnetohydrodynamics (MHD) simulations has greatly
improved our understanding of jet production and its dependence on black hole
spin. Simulation results show both disks and jets are sensitive to the magnetic
flux threading the accretion flow as well as possible misalignment between the
angular momentum of the accretion flow and the black hole spin. Radiation MHD
simulations are providing new insights into the stability of luminous accretion
flows and highlighting the potential importance of radiation viscosity, UV
opacity from atoms, and spiral density waves in AGNs.
