MHD numerical models for the dynamics and non-thermal emission of Pulsar Wind Nebulae

Recent results from MHD numerical models of the dynamics and non-thermal emission of Pulsar Wind Nebulae (PWNe) are discussed and presented in this Ph.D. thesis. We focused our attention to the Crab Nebula, which is the PWN prototype, and one of the most interesting and studied objects in the sky. The main topics we faced are the problem of the origin of the low energy emitting particles (connected to the role of pulsars as anti-matter factories) and the problem of the efficient particle acceleration at the pulsar wind termination shock, which produces particles up to PeV energies in one of the most hostile environment for particle acceleration.