The production of electroweak Z bosons that decay to neutrinos and recoil against jets with large transverse momentum is an important background process to searches for dark matter at the Large Hadron Collider (LHC). To fully benefit from opportunities offered by the future high-luminosity LHC, the theoretical description of the pp→Z+j process should be extended to include one of the largest remaining uncertainties, namely the mixed QCD-EW corrections. In this talk I will review the importance of measuring vector boson (Z,W,gamma) plus jet production at the LHC and show their state-of-the-art predictions. After that I will discuss our current work-in progress on computing the missing mixed QCD-EW corrections for Z+j production at large transverse momentum. This work also serves as a starting point to tackle the same corrections for W+j and gamma+j production in the future.