  Pulsar Wind Nebulae are highly intriguing astrophysical objects in many
respects. They are the brightest and closest class of relativistic sources, and
hence the ultimate laboratory for the physics of relativistic plasmas: several
processes observed (or inferred to occur) in other classes of relativistic
sources can here be studied with unique detail, like the acceleration and
collimation of relativistic outflows, or the acceleration of particles at
relativistic shocks.
  Here I review the current status of our theoretical understanding of Pulsar
Wind Nebulae in light of the most recent 2D and 3D MHD modelling of these
sources. I will discuss how these studies are taking us to the point when we
can reliably use multi-wavelength observations of these nebulae as a
diagnostics of the hidden physics of the pulsar wind and of the mechanism(s)
through which particles are accelerated at the highly relativistic shock that
terminates the wind.
  Finally I will briefly discuss recent progress in the modelling of evolved
Pulsar Wind Nebulae and of the escape of particles from these systems. This
effort is instrumental to credibly assess the role of Pulsar Winds as sources
of cosmic ray leptons, and has recently been recognised to have important
implications also on cosmic ray transport in the Galaxy.
