The purpose of this survey is two-fold, primarily to compile a selection of rings and ring constructions which distinguish radical theoretical properties of rings. This will be achieved mainly by the secondary aim which is to localize the position of most of the known radicals, in particular thatJϕ≠B(the existence of a simple primitive ring without non-zero idempotent),K≠Kp(the existence of a ringAwith zero total such that for every prime idealP(≠A) the total ofA/Pis not zero) and that(Veldsman's left superprime radical is properly contained in Olson's uniformly strongly prime radical).