  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.
