We present the structure and energetics of surface reduction and NO2 adsorption on the reduced (1 1 1), (1 1 0) and (1 0 0) surfaces of ceria using density functional theory with the generalized gradient approximations (GGA) corrected for on-site Coulomb interactions, GGA+U. Vacancy formation at the surfaces of the ceria show reduction of two neighbouring Ce atoms to Ce(III) and gap states in the electronic density of states (EDOS). This gives rise to relaxation of the surface with elongated Ce–O distances around the reduced sites. Reduction is the easiest on the (1 1 0) surface which displays two energetically similar structures with reduction of a sub-surface cerium ion in one of the cases. NO2 adsorbs strongly on the surface resulting in an asymmetric molecule with significant expansion of the N–O bonds for the oxygen that fills the vacant site. This activation of the molecule is the weakest on the (1 1 0) surface. Analysis of the electronic structure and spin density distributions demonstrates that one Ce(III) has been re-oxidised to Ce(IV), with the formation of an adsorbed NO2- species. These results allow a rationalisation of experimental findings and demonstrate the applicability of the GGA+U approach to the study of systems in which reduced ceria surfaces play a role.