OBJECTIVE Total intravenous anesthesia (TIVA) has seen several developments since it was first used. Since the synthesis of the first intravenous anesthetics, with the introduction of barbiturates (1921) and thiopental (1934), TIVA has evolved until the development of TIVA with target-controlled infusion pumps (TCI). The first pharmacokinetic model for the use of TCI was described by Schwilden in 1981. From that moment on, it was demonstrated that it is possible to maintain the desired plasma concentration of a drug using an infusion pump managed by a computer. BACKGROUND The objective of this report was to describe the theoretical bases of TCI, propose the development of a common TCI vocabulary, which has not been done in Brazil and make a critical analysis of the current aspects of TCI in the world and in Brazil. CONCLUSIONS The advent of new infusion pumps with pharmacokinetic models of remifentanil, sufentanil and propofol opens a new chapter in TIVA and aligns Brazil with the world tendency in TCI. Those systems will allow TCI of hypnotics and opioids concomitantly. However, the most important conclusion refers to the economy, since drugs used in those pumps will not be restricted to only one drug company, similar to what happened with propofol. Nowadays, TCI devices for the use of propofol and opioids, which accept any pharmaceutical presentation, with the advantage of changing the concentration of the drug in the syringe according to the dilution desired are available.