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The powerful radiative winds of hot stars with strong magnetic fields aremagnetically confined into large, corotating magnetospheres, which exertimportant influences on stellar evolution via rotational spindown and mass-lossquenching. They are detectable via diagnostics across the electromagneticspectrum. Since the fossil magnetic fields of early-type stars are stable overlong timescales, and the ion source is internal and isotropic, hot starmagnetospheres are also remarkably stable. This stability, the relative easewith which they can be studied at multiple wavelengths, and the growingpopulation of such objects, makes them powerful laboratories for plasmaastrophysics. The magnetospheres of the magnetic early B-type stars stand outfor being detectable in every one of the available diagnostics. In thiscontribution I review the basic methods by which surface magnetic fields areconstrained; the theoretical tools that have been developed in order to revealthe key physical processes governing hot star magnetospheres; and someimportant recent results and open-ended questions regarding the properties ofsurface magnetic fields and the behaviour of magnetospheric plasma.

Modelling the Magnetic Fields and Magnetospheres of Early B-Type Stars