Highly magnetized environments around compact astrophysical sources (black holes, neutron stars) and their relativistic outflows provide exquisite conditions for accelerating charged particles to very high energies (TeV to PeV and beyond; VHE) and producing multimessenger signals (e.g. photons and neutrinos). Indeed, the pervasive turbulence can ensure efficient stochastic particle acceleration, while the ambient backgrounds provide ideal targets for radiative and hadronic interactions.