Increasing the precision for $Z$ production at colliders: mixed QCD-QED effects

In this talk, we describe the recent progress on the inclusion of mixed QCD-QED corrections for collider observables. In particular, we developed a formalism to extend $q_T$-resummation to deal with simultaneous emission of gluons and photons. We applied it to $Z$ production at colliders, and briefly discuss extensions to more complicated final states.