In this talk, I will focus on the study of the leptonic decay $B\rightarrow \ell \nu_{\ell}$ at next-to-leading order in QED. The future improvements of experimental measurements of this channel require a reliable theory prediction, hence a careful theoretical estimate of QED corrections. The multi-scale character of this process requires an appropriate effective theory (EFT) construction to factorize the different contributions. In the first part of this talk, I will discuss the EFT description of the process at the partonic level, which is based on Heavy Quark Effective Theory and Soft Collinear Effective Theory. I will show how the inclusion of QED corrections demands a generalisation of the hadronic decay constant defining a new non-perturbative input. In the second part of the talk, I will discuss the EFT description below the confinement scale based on the Heavy Hadron Chiral Lagrangian and derive a factorisation formula for the decay rate. I will finally estimate the numerical impact of each contributions from this formula to the final rate and assess their associated uncertainties.