Intravenous injection of anesthetic drugs dates back to the 17 th Century when opium and chloral hydrate have been injected intravenously. It was not until the 1930s intravenous anesthesia became popular with the invention of barbiturates.Early intravenous anesthetic agents such as barbiturates were ideal for induction of anesthesia, but not suitable for maintenance of anesthesia. Most of these drugs accumulated significantly with increasing durations of infusion and also resulted in cardiorespiratory depression. The invention of propofol and shorter acting opioid analgesics such as remifentanil and alfentanil have revolutionized intravenous anesthesia. The rapid onset and offset of these drugs lends itself to being suitable agents for maintenance of anesthesia over prolonged periods of time. 1,2 Detailed understanding of the pharmacokinetics of propofol and remifentanil, combined with technological advances in intravenous pumps capable of accurate delivery of drugs have resulted in great development of the field of total intravenous anesthesia and target controlled infusions. I would like to discuss, in this article, the pharmacokinetics and pharmacokinetic models behind these intravenous infusion pumps.