The study of Computational Complexity began with the investigation of Turing machine computations with limits on the amounts of tape or time which could be used. Later a set of general axioms for measures of computation was presented and this instigated much study of the properties of these general measures. Many interesting results were shown, but the general axioms allowed measures with undesirable properties and several attempts have been made to tighten up the axioms so that only desirable measures will be defined.