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.
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