Soft Collinear Effective Theory (SCET) formalism has been successfully applied to a number of important observables in collider physics improving the accuracy of fixed-order predictions via the leading power resummation of large logarithmic contributions which appear in certain regions of phase space. Recently, a renewed interest in subleading power corrections has arisen in the theoretical community. In this talk, I will discuss the framework for the threshold resummation of the Drell-Yan process and Higgs production via gluon fusion at next-to-leading power using SCET. I will prove the general factorisation formula and explain the new objects that emerge beyond leading power: collinear jet functions and generalized soft functions. The ingredients necessary to perform leading logarithmic resummation at next-to-leading power will be shown and I will present selected fixed order results.