  Interaction with the Interstellar Medium (ISM) cannot be ignored in
understanding planetary nebula (PN) evolution and shaping. In an effort to
understand the range of shapes observed in the outer envelopes of PNe, we have
run a comprehensive set of three-dimensional hydrodynamic simulations, from the
beginning of the asymptotic giant branch (AGB) superwind phase until the end of
the post--AGB/PN phase. A 'triple-wind' model is used, including a slow AGB
wind, fast post--AGB wind and third wind reflecting the linear movement through
the ISM. A wide range of stellar velocities, mass-loss rates and ISM densities
have been considered. We find ISM interaction strongly affects outer PN
structures, with the dominant shaping occuring during the AGB phase. The
simulations predict four stages of PN--ISM interaction whereby the PN is
initially unaffected (1), then limb-brightened in the direction of motion (2),
then distorted with the star moving away from the geometric centre (3) and
finally so distorted that the object is no longer recognisable as a PN and may
not be classed as such (4). Parsec-size shells around PN are predicted to be
common. The structure and brightness of ancient PNe is largely determined by
the ISM interaction, caused by rebrightening during the second stage; this
effect may address the current discrepancies in Galactic PN abundance. The
majority of PNe will have tail structures. Evidence for strong interaction is
found for all known planetary nebulae in globular clusters.
