We discuss the role of particle-in-cell (PIC) simulations in unveiling the
origin of the emitting particles in PWNe. After describing the basics of the
PIC technique, we summarize its implications for the quiescent and the flaring
emission of the Crab Nebula, as a prototype of PWNe. A consensus seems to be
emerging that, in addition to the standard scenario of particle acceleration
via the Fermi process at the termination shock of the pulsar wind, magnetic
reconnection in the wind, at the termination shock and in the Nebula plays a
major role in powering the multi-wavelength signatures of PWNe.Comment: 32 pages, 16 figures, to appear in the book "Modelling Nebulae"
edited by D. Torres for Springer, based on the invited contributions to the
workshop held in Sant Cugat (Barcelona), June 14-17, 201