The effect of Fock exchange on the periodic description of the geometrical structure, elastic constants, and electronic and magnetic properties of NiO is analyzed. Hybrid density functionals which combine a portion of "exact" Fock exchange with conventional local density approximation (LDA) or generalized gradient approximation (GGA) functionals remedy a number of serious inconsistencies with the traditional LDA or GGA descriptions of this prototypical "Mott" insulator. For example, the hybrid B3LYP functional (which mixes ∼20% Fock exchange with GGA functionals) introduces a significant insulating gap and yields antiferromagnetic Heisenberg coupling constants between Ni sites (J 2 ) in semiquantitative agreement with experiment. Closer inspection shows that while the B3LYP orbital band gap is in excellent agreement with experiment, the magnitude of the antiferromagnetic coupling is overestimated by slightly more than 50%. This has led us to examine a simplified model which combines Fock exchange with the LDA exchange and correlation functionals. This combination allows us to study the magnitude and nature of the band gap, the magnitude of the unpaired spin densities in the different magnetic phases, and the two most important magnetic coupling constants as a function of the fraction of Fock exchange included. It is concluded that ∼35% Fock exchange gives a reasonably balanced description of all properties, including structural parameters, magnetic form factors, the antiferromagnetic Ni-Ni exchange constant, and the character and magnitude of the band gap.