The inclusive production cross sections for forward jets, as well for jets in dijet events with at least one jet emitted at central and the other at forward pseudorapidities, are measured in the range of transverse momenta p(T) = 35-150 GeV/c in proton-proton collisions at root s = 7 TeV by the CMS experiment at the LHC. Forward jets are measured within pseudorapidities 3.2<|eta|<4.7, and central jets within the |eta|<2.8 range. The double differential cross sections with respect to pt and eta are compared to predictions from three approaches in perturbative quantum chromodynamics: (i) next-to-leading-order calculations obtained with and without matching to parton-shower Monte Carlo simulations, (ii) PYTHIA and HERWIG parton-shower event generators with different tunes of parameters, and (iii) CASCADE and HEJ models, including different non-collinear corrections to standard single-parton radiation. The single-jet inclusive forward jet spectrum is well described by all models, but not all predictions are consistent with the spectra observed for the forward-central dijet events. RI Azzi, Patrizia/H-5404-2012; Lokhtin, Igor/D-7004-2012; Torassa, Ezio/I-1788-2012