Particle acceleration in Pulsars and PWNe

Pulsar wind nebulae are among the most efficient and at the same time most mysterious accelerators in Nature. These objects reveal the presence of leptons accelerated up to PeV energies and acceleration efficiencies up to 30%. In spite of this, the mechanisms by which particles are accelerated inside them remain poorly understood. Acceleration certainly takes place in the pulsar magnetosphere, but most of the energetic particles we directly observe, through the bright synchrotron and Inverse Compton emission that characterizes these nebulae, are thought to be accelerated at the pulsar wind termination shock. This is believed to be the most extreme example of a magnetized relativistic shock, and as such a poor accelerator. In these lectures I will review the processes that have been proposed to solve this puzzle and their current assessment.