Accretion onto compact objects is one of nature’s most efficient engines, powering neutron stars and both stellar-mass and supermassive black holes (BHs). The radiation and particles released as matter spirals inward encode the microphysics of plasma under extreme gravitational and electromagnetic fields, as well as the properties of the compact objects themselves. Yet disentangling these signals remains challenging because the channels that convert accretion power into radiation and outflows are still debated. The last decade has transformed the field. Micro- arcsecond imaging, and X-ray polarimetry now probe accretion flows and relativistic outflows with unprecedented fidelity, while posing new puzzles. High-energy neutrinos (IceCube, KM3NeT) have been associated with accreting supermassive BHs. TeV–PeV gamma-rays (HAWC, H.E.S.S., LHAASO) from some stellar-mass BH systems mark them as promising factories of high-energy cosmic rays. Meanwhile, IXPE polarimetry and EHT imaging are beginning to map the geometry and magnetic structure of the plasma near the event horizon.

A unifying question emerges: What specific conditions in BH magnetospheres, inflows and outflows, enable the efficient production of very-high-energy photons, neutrinos, and cosmic rays? The program will bring together theorists and observers working on BH magnetospheres, from GRMHD and kinetic plasma physics to radiation transport, neutrino and cosmic ray astrophysics, and time-domain, multi-wavelength observations.