Total intravenous anaesthesia (TIVA) is becoming increasingly popular among anaesthetists. It has several advantages, namely each component of the anaesthetic protocol can be independently controlled, and the operating room remains unpolluted with nitrous oxide or volatile anaesthetic agents. TIVA aims to maintain a constant blood concentration of each anaesthetic agent. This means that infusion rates need to be repeatedly altered. A computer calculates theoretical blood concentrations of agent according to a pharmacokinetic model, and drives an infusion device. Only a few programmes have been developed by research teams. No commercial device is available as yet. However, there are several syringe pumps and volumetric pumps which are accurate enough for use in TIVA and which may be controlled by computer. Clinical studies have shown the benefits of TIVA: greater haemodynamic stability, decreased drug consumption, more rapid recovery, and a lesser need for postoperative ventilatory support. The most appropriate agents are propofol and etomidate as hypnotics, alfentanil and sufentanil for opioids, vecuronium and atracurium as muscle relaxants. Etomidate is not recommended for prolonged infusions, because of the risk of adrenocortical suppression. TIVA seems to be attractive for neurosurgery, thoracic surgery, day case surgery, endoscopic procedures, and anaesthesia in remote locations. Unfortunately, it is an expensive technique. Moreover, there is considerable interpatient variability of the drug concentration required for a same clinical effect. Two methods are proposed to decrease this variability: population pharmacokinetic models and Bayesian forecasting. Closed loop systems are still research tools. It is concluded that computer-driven anaesthesia is the equivalent to the vaporizer for volatile agents. However, further clinical studies are needed to determine whether the advantages of this technique outweigh its disadvantages.