Several popular exact methods of the light scattering theory, namely the separation of variables, extended boundary condition and point matching ones, involve (single) expansions of the fields in terms of wave functions. So far the spherical functions were basically applied within these methods. We consider the main features of application of the spheroidal functions in the general case of non-spheroidal scatterers. Our consideration is based on several codes that were recently developed by using an original approach efficient for scatterers of high eccentricity and on special theoretical analysis of the applicability ranges of the methods.