  Pulsed emission from gamma-ray pulsars originates inside the magnetosphere,
from radiation by charged particles accelerated near the magnetic poles or in
the outer gaps. In polar cap models, the high energy spectrum is cut off by
magnetic pair production above an energy that is dependent on the local
magnetic field strength. While most young pulsars with surface fields in the
range B = 10^{12} - 10^{13} G are expected to have high energy cutoffs around
several GeV, the gamma-ray spectra of old pulsars having lower surface fields
may extend to 50 GeV. Although the gamma-ray emission of older pulsars is
weaker, detecting pulsed emission at high energies from nearby sources would be
an important confirmation of polar cap models. Outer gap models predict more
gradual high-energy turnovers at around 10 GeV, but also predict an inverse
Compton component extending to TeV energies. Detection of pulsed TeV emission,
which would not survive attenuation at the polar caps, is thus an important
test of outer gap models. Next-generation gamma-ray telescopes sensitive to
GeV-TeV emission will provide critical tests of pulsar acceleration and
emission mechanisms.
