  We discuss recent progress concerning the resummation of large logarithms at
next-to-leading power (NLP) in scattering processes such as Drell-Yan and deep
inelastic scattering near threshold, and thrust in the two-jet limit. We start
by reviewing the approach based on soft-collinear effective field theory and
show that the standard factorization into short distance coefficients,
collinear and soft functions at NLP leads in general to the appearance of
endpoint divergences, which prevent the naive application of resummation
techniques based on the renormalization group. Taking thrust as a case study,
we then show that these singularities are indeed an artifact of the effective
theory, and discuss how they can be removed to recover a finite factorization
theorem and achieve resummation at NLP, at LL accuracy. Last, we discuss recent
work concerning the calculation of all collinear and soft functions necessary
to reproduce Drell-Yan near threshold up to NNLO in perturbation theory. This
calculation provides useful data to extend resummation at NLP beyond LL
accuracy.
