We experience the interaction of waves with obstacles several 
times in our daily lives; the waves could be
light, sound, pressure or elastic waves, to name but a few possibilities. 
The study of these interactions has long
fascinated mankind, and led to some very interesting mathematical 
developments.

         In this talk, we shall survey some of the history behind 
computational scattering. We shall then focus on
some central challenges which remain in the field, and describe some 
promising approaches to their resolution.