I review the status of perturbative QCD calculations for jet production in eP -scattering at HERA. I will discuss possibilities of combining fixed order, especially higher order, calculations and parton showers. ¶ Invited talk at the Ringberg Workshop New Trends in HERA Physics 2001, Ringberg Castle, Tegernsee, Germany, 17–22 June 2001 Jet Production at HERA Björn Pötter§ Max-Planck-Institut fü...