  We review the recent advances in the pulsar high-energy $\gamma$-ray
observation and the electrodynamics of the pulsar magnetospheres from the early
vacuum model to the recent plasma-filled models by the numerical simulations.
The numerical simulations have made the significant progresses toward the
self-consistent modeling of the plasma-filled magnetosphere by including the
particle acceleration and radiation. The current numerical simulations confirm
a near force-free magnetosphere with the particle acceleration in the
separatrix near the light cylinder and the current sheet outside the light
cylinder, which can provide a good match to the recent high-energy $\gamma$-ray
observations. The modeling of the combined multi-wavelength light curves,
spectra, and polarization are expected to provide a stronger constrain on the
geometry of the magnetic field lines, the location of the particle acceleration
and the emission region, and the emission mechanism in the pulsar
magnetospheres.
