The capability for a dialysis machine to use a measurement of the patient's status to automatically tune the dialysis session on-line is commonly addressed by physicians and bioengineers working in the hemodialysis field as "biofeedback." This paper presents the basics of mathematical modeling and control theory normally used in bioengineering, together with some advanced techniques, such as adaptive and multi-input/multi-output control systems. The architectural requirements for implementing biofeedback techniques in renal replacement therapy are then discussed, with due attention paid to the safety aspects, which play a central role in machines hosting such new techniques as well as their therapeutic mission. Finally, the blood volume tracking system, which is aimed at performing the intradialytic water removal, while maintaining a balance inside the body fluids compartments and thus preserving cardiovascular stability, is used as a paradigmatic example of such a class of advanced techniques. The significant results shown by the blood-volume-controlled treatments during a multicenter study focused on its clinical application (30% reduction of intradialysis collapses, 13% reduction of interdialysis symptoms) indicate the technical feasibility and the remarkable benefits of such systems, which get closer to a structurally complete artificial kidney. (C) 1999 by the National Kidney Foundation, Inc.