  Exact solutions exist which describe impulsive gravitational waves
propagating in Minkowski, de Sitter, or anti-de Sitter universes. These may be
either nonexpanding or expanding. Both cases in each background are reviewed
here from a unified point of view. All the main methods for their construction
are described systematically: the Penrose "cut and paste" method, explicit
construction of continuous coordinates, distributional limits of sandwich
waves, embedding from higher dimensions, and boosts of sources or limits of
infinite accelerations.
  Attention is concentrated on the most interesting specific solutions. In
particular, the nonexpanding impulsive waves that are generated by null
multipole particles are described. These generalize the well-known
Aichelburg-Sexl and Hotta-Tanaka monopole solutions. Also described are the
expanding spherical impulses that are generated by snapping and colliding
strings. Geodesics and some other properties of impulsive wave spacetimes are
also summarized.
