  Recent results of the event horizon-scale images of M87* and Sagittarius A*
from the Event Horizon Telescope Collaboration show that strong magnetic fields
are likely present around the central black holes (BHs) in these sources.
Magnetically arrested disks (MADs), the end stage of magnetic flux saturation
around BHs, are especially rich in horizon-scale physics due to the presence of
powerful jets and magnetic flux eruptions that provide significant feedback on
the accretion mechanism. Here, we present an overview of our current knowledge
about the magnetic field evolution in numerical simulations of accreting BHs,
focusing on jet launching, black hole-interstellar medium feedback, and black
hole imaging of MADs. We find that misaligned MAD accretion flows seemingly
exhibit jet ejection cycles that could produce flaring states in radio-quiet
active galactic nuclei. Further, we show that advances in horizon-scale
interferometric telescopes could identify disk misalignment by imaging the
disk-jet connection region.
