Computer controls are increasingly being employed in systems ranging from simple to very complex. A new trend is to extend these computer systems to include monitoring schemes to detect malfunctions. An example is provided by new automobiles sold in the US, Canada, and Europe. By law they must include “on-board diagnostics” designed to detect certain malfunctions in the powertrain system that may cause excessive emissions. The present article outlines some of the fundamental concepts of system's monitoring and general principles for the design of such monitors.