Target controlled infusion (TCI) is a clinically-available and widely-used computer-controlled method of drug administration, adjusting the drug titration towards user selected plasma- or effect-site concentrations, calculated according to pharmacokinetic-pharmacodynamic (PKPD) models. Although this technology is clinically available for several anaesthetic drugs, the contemporary commercialised PKPD models suffer from multiple limitations. First, PKPD models for anaesthetic drugs are developed using deliberately selected patient populations, often excluding the more challenging populations, such as children, obese or elderly patients, of whom the body composition or elimination mechanisms may be structurally different compared to the lean adult patient population. Separate PKPD models have been developed for some of these subcategories, but the availability of multiple PKPD models for a single drug increases the risk for invalid model selection by the user. Second, some models are restricted to the prediction of plasma-concentration without enabling effect-site controlled TCI or they identify the effect-site equilibration rate constant using methods other than PKPD modelling. Advances in computing and the emergence of globally collected databases has allowed the development of new “general purpose” PKPD models. These take on the challenging task of identifying the relationships between patient covariates (age, weight, sex, etc) and the volumes and clearances of multi-compartmental pharmacokinetic models applicable across broad populations from neonates to the elderly, from the underweight to the obese. These models address the issues of allometric scaling of body weight and size, body composition, sex differences, changes with advanced age, and for young children, changes with maturation and growth. General purpose models for propofol, remifentanil and dexmedetomidine have appeared and these greatly reduce the risk of invalid model selection. In this narrative review, we discuss the development, characteristics and validation of several described general purpose PKPD models for anaesthetic drugs.