  There is considerable controversy about the size and importance of
nonperturbative contributions to the evolution of transverse-momentum-dependent
(TMD) parton distribution functions. Standard fits to relatively high-energy
Drell-Yan data give evolution that when taken to lower Q is too rapid to be
consistent with recent data in semi-inclusive deeply inelastic scattering. Some
authors provide very different forms for TMD evolution, even arguing that
nonperturbative contributions at large transverse distance b_T are not needed
or are irrelevant. Here, we systematically analyze the issues, both
perturbative and nonperturbative. We make a motivated proposal for the
parameterization of the nonperturbative part of the TMD evolution kernel that
could give consistency: with the variety of apparently conflicting data, with
theoretical perturbative calculations where they are applicable, and with
general theoretical nonperturbative constraints on correlation functions at
large distances. We propose and use a scheme- and scale-independent function
A(b_T) that gives a tool to compare and diagnose different proposals for TMD
evolution. We also advocate for phenomenological studies of A(b_T) as a probe
of TMD evolution. The results are important generally for applications of TMD
factorization. In particular, they are important to making predictions for
proposed polarized Drell-Yan experiments to measure the Sivers function.
