In the first part of my talk, I will explain the essential ingredients of SCET formalism needed for the next-to-leading power factorization and resummation. In particular, I will show how to factorize time-ordered products of subleading Lagrangians. I will define the so-called "generalized soft functions" and present their renormalization properties, pointing out the differences with the case of the leading-power soft functions. In the second part, I will show numerical results for the Higgs production cross-section, and discuss the ambiguity related to the choice of the soft scale. Finally, I will point out the significant obstacles that currently prevent straightforward computations of the next-to-leading logarithmic corrections beyond leading power.