Precise predictions for the production of jets in deep inelastic scattering

We give an overview of our calculation of jet-production processes in deep-inelastic lepton-proton scattering (DIS) at O(α3s) both for the neutral- and the charged-current cases. Phenomenological results are presented for di-jet production at next-to-next-to-leading order (NNLO) and inclusive-jet production at N3LO, which are compared to experimental measurements performed at HERA. The inclusion of higher-order corrections result in a substantial reduction of residual theory uncertainties and exhibit an improved agreement with data. These results pave the way for precision phenomenology using jet observables at future lepton-proton colliders.