List of problems for future research in generalized Lorenz-Mie theories and related topics, review and prospectus [invited].

The expression "generalized Lorenz-Mie theories" generically denotes a class of light-scattering theories describing the interaction between an illuminating electromagnetic arbitrary-shaped beam and a particle possessing a high degree of symmetry. This allows one to use the method of separation of variables in which the illuminating beam is expressed as an expansion over a set of basis functions. Such theories have been derived and applied over the past 35 years. Although, as a whole, these theories are now well developed, there remains a list of problems to be solved, some of which are described in this paper.