Modeling Pulsar Wind Nebulae

In the last few years, new observations by CHANDRA and XMM have shown that Pulsar Wind Nebulae present complex but similar inner features, with the presence of axisymmetric rings and jets, which are generally referred to as a jet-torus structure. Due to the rapid growth in accuracy and robustness of numerical schemes for relativistic fluid-dynamics, it is now possible to model the flow and magnetic structure of the relativistic plasma responsible for the emission. Recent results have clarified how the jet and rings are formed, suggesting that the morphology is strongly related to the wind properties, so that, in principle, it is possible to infer the conditions in the unshocked wind from the nebular emission. I will review here the current status in the modeling of Pulsar Wind Nebulae, and, in particular, how numerical simulations have increased our understanding of the flow structure, observed emission, polarization and spectral properties. I will also point to possible future developments of the present models.