  The powerful radiative winds of hot stars with strong magnetic fields are
magnetically confined into large, corotating magnetospheres, which exert
important influences on stellar evolution via rotational spindown and mass-loss
quenching. They are detectable via diagnostics across the electromagnetic
spectrum. Since the fossil magnetic fields of early-type stars are stable over
long timescales, and the ion source is internal and isotropic, hot star
magnetospheres are also remarkably stable. This stability, the relative ease
with which they can be studied at multiple wavelengths, and the growing
population of such objects, makes them powerful laboratories for plasma
astrophysics. The magnetospheres of the magnetic early B-type stars stand out
for being detectable in every one of the available diagnostics. In this
contribution I review the basic methods by which surface magnetic fields are
constrained; the theoretical tools that have been developed in order to reveal
the key physical processes governing hot star magnetospheres; and some
important recent results and open-ended questions regarding the properties of
surface magnetic fields and the behaviour of magnetospheric plasma.
