Several measurements of jet cross sections in proton-proton collisions at 5.02 and 13~TeV with the CMS experiment are presented. Jets are reconstructed using the anti-$k_T$ clustering algorithm with $R = 0.4$ and $R=0.7$. Double-differential measurements of inclusive jet production at 5.02 and 13~TeV are performed as a function of the jet transverse momentum and jet rapidity; furthermore, a triple-differential measurement as a function of leading jet transverse momentum, dijet azimuthal correlations, and jet multiplicity and a double-differential measurement as a function of jet multiplicity and single-jet transverse momentum are also provided for multijet production at 13~TeV. The measured jet cross sections are corrected for detector effects and compared with the predictions from perturbative QCD. Finally, a QCD interpretation of the inclusive jet measurement with $R=0.7$ at 13 TeV is also presented.