MHD interaction of pulsar wind nebulae with SNRs and with the ISM

I will review our current understanding of the different evolutionary stages of a pulsar wind nebula as it is interacting with its associated supernova remnant. Therefore, I will discuss both analytical and more recent numerical (M)HD models. The four main stages of a pulsar wind nebula are: the supersonic expansion stage, the reverse shock interaction stage, the subsonic expansion stage and ultimately the stage when the head of the bubble is bounded by a bow shock, due to the supersonic motion of the pulsar. Ultimately this pulsar wind nebula bow shock will break through its associated remnant, after which the pulsar-powered bow shock will interact directly with the interstellar medium. I will discuss recent numerical models from these type of pulsar wind nebulae and their morphology.