A general theorem on the GBDT version of the B\"acklund-Darboux
transformation for systems rationally depending on the spectral parameter is
treated and its applications to nonlinear equations are given. Explicit
solutions of direct and inverse problems for Dirac-type systems, including
systems with singularities, and for the system auxiliary to the $N$-wave
equation are reviewed. New results on explicit construction of the wave
functions for radial Dirac equation are obtained.