Precise theoretical predictions are a key ingredient in ongoing tests of the Standard Model and in searches for physics beyond it. Since its inception twenty years ago, Soft Collinear Effective Theory (SCET) has been successfully applied to improve the precision of many important observables in collider physics. It is now standard practice to use SCET to derive factorisation theorems and apply renormalisation group (RG) methods to achieve leading power resummation of large logarithms that appear in regions of phase space with disparate energy scales. In this talk, I will discuss the recent advances in taking the step beyond the leading term in the power expansion. Focusing on the threshold Drell-Yan process, I will explain how the general factorisation formula can be derived and I will discuss new objects that emerge beyond leading power: collinear jet functions and generalised soft functions.
I will present the leading logarithmic solution of the RG equations and explain challenges in increasing the logarithmic accuracy of resummation at next-to-leading power.
