We present new parton distribution functions (PDFs) at next-to-next-to-leading order (NNLO) from the CTEQ-TEA global analysis of quantum chromodynamics. These differ from previous CT PDFs in several respects, including the use of data from LHC experiments and the new D0 charged-lepton rapidity asymmetry data, as well as the use of a more flexible parametrization of PDFs that, in particular, allows a better fit to different combinations of quark flavors. Predictions for important LHC processes, especially Higgs boson production at 13 TeV, are presented. These CT14 PDFs include a central set and error sets in the Hessian representation. For completeness, we also present the CT14 PDFs determined at the LO and the NLO in QCD. Besides these general-purpose PDF sets, we provide a series of (N)NLO sets with various αs values and additional sets in general-mass variable flavor number schemes, to deal with heavy partons, with up to three, four, and six active flavors.