The immediate vicinity of black holes provides exquisite conditions for accelerating particles to extremely high energies, up to PeV and beyond. One likely mechanism is via the collisionless plasma turbulence that is expected in the black hole environment, and whose random electromagnetic fields promote efficient stochastic particle acceleration (diffusion in energy space). Accelerated particles add viscosity to the flow, and therefore damp the turbulence that feeds them, giving rise to an interesting nonlinear interaction between particles and electromagnetic fields.