  It is widely believed that some classes of high-energy transients may be
powered by the rotational energy of a rapidly spinning black hole. The energy
extraction mechanism commonly discussed involves macroscopic magnetic fields
that are produced by currents flowing in a disk or torus surrounding the black
hole. In spite of large efforts that have led to impressive progress in our
understanding of the physics of magnetized flows in Kerr geometry, several
important issues remain unresolved: the nature of the load in the
Blandford-Znajeck model, the causality and stability of a force-free
magnetosphere, global current closure, and the role of boundary conditions on
the channels through which the extracted energy is released. This chapter
provides an account of recent work that addresses some of those open questions.
