We discuss growing evidence that pulsar high energy emission is generated via Inverse Compton mechanism. We reproduce the broadband spectrum of Crab pulsar, from UV to very high energy gamma-rays - nearly ten decades in energy, within the framework of the cyclotron-self-Compton model. Emission is produced by two counter-streaming beams within the outer gaps, at distances above ~ 20 NS radii. The scattering occurs in the deep Klein-Nishina regime, whereby the IC component provides a direct measurement of particle distribution within the magnetosphere. The required plasma multiplicity is high, ~ 106-7, but is consistent with the average particle flux injected into the pulsar wind nebula.

Secondly, recent observations of flares in the Crab nebula call into question the prevalent model of particle acceleration in relativistic astrophysical environments, the stochastic shock acceleration. Magnetic reconnection is likely to play an important, and perhaps a dominant role.