  Force-Free Electrodynamics (FFE) describes magnetically dominated
relativistic plasma via non-linear equations for the electromagnetic field
alone. Such plasma is thought to play a key role in the physics of pulsars and
active black holes. Despite its simple covariant formulation, FFE has primarily
been studied in 3+1 frameworks, where spacetime is split into space and time.
In this article we systematically develop the theory of force-free
magnetospheres taking a spacetime perspective. Using a suite of spacetime tools
and techniques (notably exterior calculus) we cover 1) the basics of the
theory, 2) exact solutions that demonstrate the extraction and transport of the
rotational energy of a compact object (in the case of a black hole, the
Blandford-Znajek mechanism), 3) the behavior of current sheets, 4) the general
theory of stationary, axisymmetric magnetospheres and 5) general properties of
pulsar and black hole magnetospheres. We thereby synthesize, clarify and
generalize known aspects of the physics of force-free magnetospheres, while
also introducing several new results.
