  We review recent theoretical developments on pulsar winds, their nebulae and
relativistic shock acceleration, and show how they illuminate unsolved problems
in plerion spectra, in particular the multiple spectral breaks in the Crab and
the low-frequency breaks of plerions such as G 21.5-0.9 and 3C 58. Recent work
on Fermi acceleration theory at relativistic shocks shows that a particle
spectral index of 2.2-2.3, compatible with the X-ray spectra of plerions,
results under a wide variety of assumptions. If pulsar winds contain ions as
well as electrons and positrons, the mechanism of Hoshino et al. (1992), which
yields harder spectra, would operate at lower energies and may explain the flat
radio spectral indices of plerions. This scenario implies wind parameters in
the Crab compatible with the pulsar wind acceleration model of Lyubarsky & Kirk
(2001). Recent hydrodynamical simulations of plerion evolution inside SNR blast
waves demonstrate that the passage of the reverse shock rapidly compresses the
plerion. Using a simple isobaric model, we investigate the influence of the
resulting magnetic field compression and decrease in shock radius on the
evolution of the plerion spectrum. We suggest that the passage of the reverse
shock may explain the low-frequency breaks in 3C 58 and G 21.5-0.9, as well as
the increase in 3C 58's radio flux.
