  We develop a consistent treatment of disorder effects in strong coupling
superconductors. We use two different approaches, starting either from above or
below the transition temperature, and show their equivalence. The normal state
approach is a natural extension of a recently developed non-perturbative
resummation technique. For the superconducting state we extend the standard
Eliashberg theory to include disorder effects. We obtain a compact set of
equations which are physically transparent and easy to use. They correctly
reproduce the usual strong coupling results and disordered perturbation theory
results in the appropriate limits. We numerically solve these equations to
obtain transition temperature as a function of disorder for different phonon
couplings.
