Singularities of continuation of wave fields

The state of the art of the problem of the analytical continuation of wave fields is reviewed. The problem is a multi- disciplinary subject which involves radiophysics, acoustics, and opticsontheonehand,andmathematicalphysicsandthetheory of differential equation, on the other. The qualitative aspects of the problem are examined. A computational algorithm for field singularities is given. The relation between the singularities and the 'computational catastrophes' of scattering models is dis- cussed. To illustrate the theoretical material, numerous exam- ples are discussed in great detail.