The off-shell modelling of top-quark processes at high energies is essential to have realistic and accurate predictions to compare with data. In order to illustrate the relevant aspects of the off-shell description including QCD and electroweak radiative corrections, we present the calculation of off-shell tZj production at the LHC in the three-lepton decay channel, and of t$\bar{\rm t}$ at future lepton colliders in the semi-leptonic decay channel.