  We review the present status of QCD corrections to weak decays beyond the
leading logarithmic approximation including particle-antiparticle mixing and
rare and CP violating decays. After presenting the basic formalism for these
calculations we discuss in detail the effective hamiltonians for all decays for
which the next-to-leading corrections are known. Subsequently, we present the
phenomenological implications of these calculations. In particular we update
the values of various parameters and we incorporate new information on m_t in
view of the recent top quark discovery. One of the central issues in our review
are the theoretical uncertainties related to renormalization scale ambiguities
which are substantially reduced by including next-to-leading order corrections.
The impact of this theoretical improvement on the determination of the
Cabibbo-Kobayashi-Maskawa matrix is then illustrated in various cases.
