  The magnetospheres of neutron stars provide a valuable testing ground for
as-yet unverified theoretical predictions of quantum electrodynamics (QED) in
strong electromagnetic fields. Exhibiting magnetic field strengths well in
excess of a TeraGauss, such compact astrophysical environments permit the
action of exotic mechanisms that are forbidden by symmetries in field-free
regions. Foremost among these processes are single-photon pair creation, where
a photon converts to an electron-positron pair, and magnetic photon splitting,
where a single photon divides into two of lesser energy via the coupling to the
external field. The pair conversion process is exponentially small in weak
fields, and provides the leading order contribution to vacuum polarization. In
contrast, photon splitting possesses no energy threshold and can operate in
kinematic regimes where the lower order pair conversion is energetically
forbidden. This paper outlines some of the key physical aspects of these
processes, and highlights their manifestation in neutron star magnetospheres.
Anticipated observational signatures include profound absorption turnovers in
pulsar spectra at gamma-ray wavelengths. The shapes of these turnovers provide
diagnostics on the possible action of pair creation and the geometrical locale
of the photon emission region. There is real potential for the first
confirmation of strong field QED with the new GLAST mission, to be launched by
NASA in 2008. Suppression of pair creation by photon splitting and its
implications for pulsars is also discussed.
