The electronic structure near defects (such as impurities) in supercon
ductors is explored using a fully self-consistent technique. This tech
nique exploits the short-range nature of the impurity potential and of
the induced change in the superconducting order parameter to calculat
e features in the electronic structure down to the atomic scale with u
nprecedented spectral resolution. Magnetic and nonmagnetic static impu
rity potentials are considered, as well as local alterations in the pa
iring interaction. Extensions to strong-coupling superconductors and s
uperconductors with anisotropic order parameters are formulated.