  This paper is a review of some of the recent modeling efforts to improve our
understanding of structure formation and evolution of planetary nebulae
including their interaction with the interstellar medium. New propositions have
been made for the formation mechanism of multi-polar PNe and PPNe. These
mechanisms are based on the central engine with interacting binary stars or
hole producing instabilities in expanding shock waves leading to illumination
effects from the central star that change the appearance of the nebula.
Furthermore, there has been a lot of progress in the observation and 3D
modeling of the kinematics, which is key to the understanding of the dynamics.
Extensive observational catalogs are coming online for the kinematics, as well
as some very detailed proper motion measurements have been made. New techniques
for morpho--kinematic 3D modeling help to make the interpretation of kinematic
data more reliable and detailed. In addition to individual pointed
observations, new surveys have lead to the discovery of many PNe that show
clear signs of interaction with the interstellar medium. Systematic
hydrodynamic models of the interaction have produced a general scheme for the
observed structure that results from the interaction of an evolving planetary
nebula with the ISM. Detailed modeling of the dust-gas dynamics during the
interaction with the ISM have produced interesting predictions for future IR
observations. Detailed models were worked out for the structure of the bowshock
and tail of Mira that was recently discovered in the UV.
