The unexpected discovery of gamma-ray flares from the Crab Nebula may have surprising implications for plasma astrophysics. Standard particle acceleration mechanisms cannot account for the energies of the flaring photons. Instead, these observations point toward an acceleration process involving rapid destruction of magnetic field through reconnection. I will discuss the extreme particle acceleration process that may lead to the flares, and the likely role of current-driven instabilities in triggering reconnection in the Crab and elsewhere.