  We present a unified derivation of the resummation of Sudakov logarithms,
directly from the factorization properties of cross sections in which they
occur. We rederive in this manner the well-known exponentiation of leading and
nonleading logarithmic enhancements near the edge of phase space for cross
sections such as deeply inelastic scattering, which are induced by an
electroweak hard scattering. For QCD hard-scattering processes, such as
heavy-quark production, we show that the resummation of nonleading logarithms
requires in general mixing in the space of the color tensors of the hard
scattering. The exponentiation of Sudakov logarithms implies that many weighted
cross sections obey particular evolution equations in momentum transfer, which
streamline the computation of their Sudakov exponents. We illustrate this
method with the resummation of soft-gluon enhancements of the inclusive
Drell-Yan cross section, in both DIS and $\overline{{\rm MS}}$ factorization
schemes.
