The study of quantum-information observables at the TeV scale has intensified the focus on precision measurements of the spin structure of weak-boson pairs at the LHC. We show that a robust spin interpretation of diboson events demands an accurate determination of joint polarisation fractions and of the off-diagonal entries of the spin-density matrix. This requires the inclusion of higher-order electroweak and QCD corrections, both in and beyond the Standard Model. We summarise recent progress in the calculation of spin correlations for inclusive WZ production, including NNLO QCD + NLO EW predictions in the Standard Model and NLO QCD predictions in the Standard Model Effective Field Theory. All results are presented in realistic kinematic setups relevant for the interpretation of LHC Run-2 and Run-3 data