The extraction of weak-boson polarisation at the LHC constitutes a crucial test of the Standard Model. To that end, precise theoretical predictions as well as new methods are needed in order to exploit the maximum information available in data. In this presentation, I discuss the computation of polarised W+j production at the LHC up to next-to-next-to-leading order in QCD and show that higher orders are crucial for the precise determination of polarisation. In the second part, I introduce a new method to extract boson polarisation with the help of amplitudes and machine learning.
