In jet production in eP collisions at HERA, three kinematical regions can be distinguished. These are the photoproduction, low Q 2 and high Q 2 (deep-inelastic scattering, DIS) regimes. I review the theoretical tools for describing these regions, with special emphasis on the status of next-to-leading order calculations. I show comparisons of the theoretical calculations to data from H1 and ZEUS and discuss the consequences especially for the photon structure. In the second part of the talk I outline a possibility of improving the
theoretical tools by combining matrix elements at next-to-leading order with parton showers.