Recent measurements based on jet production in high energy pp collisions at the CERN LHC with the CMS detector are reported. Specifically, the measurement of the inclusive jet production cross section as a function of the anti-$k_t$ distance parameter $R$ divided by the jet cross section at $R = 0.4$, is discussed. The cross section ratio is sensitive to various perturbative and non-perturbative treatments of the jet formation process in quantum chromodynamics (QCD). In the second study, the regimes of validity of the parton shower and matrix element approaches are tested on multijet events in pp collisions at $\sqrt{s} = 8$ and $13$ TeV. Special attention is given to the second and third leading $p_\text{T}$ jets and their momenta and rapidity--azimuth correlations. Finally, studies of dijet production where the two leading $p_T$ jets are separated by a large pseudorapidity interval void of charged particles is presented. This signature is expected from hard color singlet exchange (two-gluon exchange in perturbative QCD). The latter can be treated with perturbative QCD techniques based on the Balitsky--Fadin--Kuraev--Lipatov (BFKL) evolution equations.