As black holes accrete surrounding gas, they often produce
relativistic, collimated outflows, or jets. Since jets form near a
black hole, they can be powerful probes of strong-field gravity.
However, how jet properties (e.g., jet power) connect to those of the
accretion flow (e.g., mass accretion rate) and the black hole (e.g.,
black hole spin) remains an area of active research. This is because
what sets the strength of large-scale magnetic flux threading the
black hole and the jet power is not understood. Recently, using
first-principles general relativistic magnetohydrodynamics (GRMHD)
computer simulations, I demonstrated that accretion disks can
accumulate large-scale magnetic flux on the black hole until the flux
becomes so strong that it obstructs gas infall and leads to a
magnetically-arrested disk (MAD). In MADs, both the black hole
magnetic flux and jet power are at their maximum, well-defined values.
I will review the emerging observational evidence for MADs in
radio-loud active galactic nuclei, jetted tidal disruptions, and
gamma-ray bursts. The abundance of MADs opens up a new vista in the
measurements of black hole masses and spins and in quantitative tests
of black accretion and jet theory. I will finish by describing the
ongoing effort at developing the next-generation GRMHD codes that will
enable us to compute detailed radiative signatures of accreting black
holes and make a more realistic than ever connection to observations.