The latest results from the H1 and ZEUS collaborations which challenge the QCD description of high energy $ep$ collisions are presented. Data from HERA continue to provide precision measurements and are compared to the latest theoretical predictions. Measurements of new processes are also presented as well as investigation of regions where perturbative QCD fails to describe the data. Four themes are presented here. Measurements of hard QCD processes, prompt photon and jet production, are used to compare to the latest theoretical predictions and, in the case of jet production, used to make high-precision extractions of the strong coupling constant up to next-next-to-leading order in QCD. All H1 and ZEUS charm and beauty cross sections in deep inelastic scattering have been combined and used to extract heavy-quark masses, including the running of the charm-quark mass with the scale of the process. Factorisation in diffraction has been investigated in charm production in deep inelastic scattering and prompt photon production in diffractive photoproduction has been measured for the first time. Finally, the inclusive data on deep inelastic scattering is presented in various forms in order to allow investigation of the underlying mechanism at very low photon virtuality $Q^2$ and low Bjorken $x$.