Density functional calculations are used to study the role of edge-functionalization on the structure and electronic properties of cycloparaphenylene (CPPs) containing from six to twenty benzenoid rings. We substitute hydrogen by the halogens fluorine, chlorine and bromine. The resultant Cyclotetrahalo-p-phenylenes are compared with their hydrogenated equivalents, related linear paraphenyl and fluoro-paraphenyl polymers, and functionalised armchair edges in graphene nanoribbons. Notably we consider both structural and electronic evolution. Finally we examine C60@[10]CPP, i.e. C60 encapsulated within [10]CPP, with the various ring terminations. The effect of halogenation on electronic level position around the gap strongly affects their capacity to form donor-acceptor pairs with fullerenes.