Cerium based intermetallic compounds exhibit a wealth of physical properties originating from the electronic states of Ce, i.e. diamagnetic Ce4+ ([Xe] 4f0), paramagnetic Ce3+ ([Xe] 4f1). Switching between the electronic states can be induced either chemically such as by inserting hydrogen, by substitutions (size effects) or physically by applying external pressure. The review exposes different classes of Ce intermetallic compounds whose properties are interpreted and/or predicted thanks to quantum computations in the framework of the density functional theoretical (DFT). Focus is broadly made on the family of the equiatomic cerium intermetallic compounds, namely ternary CeTX where T is a transition metal and X a p-element where the hydrogenation effects take a considerable place in changing the electronic configuration of Ce. Other stoichiometries of cerium intermetallic compounds with their physical properties are discussed subsequently in the later part of the review. Rather than presenting an exhaustive enumeration of stoichiometries, illustrative case studies are selected for each class of materials to provide, after presenting the experimental context, insights into original outcome from methods targeted at selective physical and chemical properties.Read less <