We review the definition of semi-inclusive jet functions within Soft Collinear Effective Theory
(SCET) and their application to inclusive jet cross sections. As an example, we consider both the
inclusive production of jets and the jet fragmentation function in proton-proton collisions. The
semi-inclusive jet functions satisfy renormalization group (RG) equations which take the form of
standard timelike DGLAP evolution equations, analogous to collinear fragmentation functions.
By solving these RG equations, the resummation of potentially large single logarithms $(\alpha_s \ln R)^n$ can be achieved. We present numerical results at NLO+NLL$_R$ accuracy and compare to existing
data from the LHC.