We present a comprehensive density functional theory+U study of the mechanisms underlying the dissociation of molecular hydrogen, and diffusion and clustering of the resulting atomic species on the CeO2(111) surface. Contrary to a widely held view based solely on a previous theoretical prediction, our results show conclusively that H2 dissociation is an activated process with a large energy barrier ∼1.0 eV that is not significantly affected by coverage or the presence of surface oxygen vacancies. The reaction proceeds through a local energy minimum - where the molecule is located close to one of the surface oxygen atoms and the H-H bond has been substantially weaken by the interaction with the substrate -, and a transition state where one H atom is attached to a surface O atom and the other H atom sits on-top of a Ce(4+) ion. In addition, we have explored how several factors, including H coverage, the location of Ce(3+) ions as well as the U value, may affect the chemisorption energy and the relative stability of isolated OH groups versus pair and trimer structures. The trimer stability at low H coverages and the larger upward relaxation of the surface O atoms within the OH groups are consistent with the assignment of the frequent experimental observation by non-contact atomic force and scanning tunneling microscopies of bright protrusions on three neighboring surface O atoms to a triple OH group. The diffusion path of isolated H atoms on the surface goes through the adsorption on-top of an oxygen in the third atomic layer with a large energy barrier of ∼1.8 eV. Overall, the large energy barriers for both, molecular dissociation and atomic diffusion, are consistent with the high activity and selectivity found recently in the partial hydrogenation of acetylene catalyzed by ceria at high H2/C2H2 ratios.