Test functions (fault detection, diagnosis, error correction, repair, etc.) that are applied concurrently while the system continues its intended function are defined as on-line testing. In its expanded scope, on-line testing includes the design of concurrent error checking subsystems that can be themselves self-checking, fail-safe systems that continue to function correctly even after an error occurs, reliability monitoring, and self-test and fault-tolerant designs. This text contains a selected set of articles that discuss many of the modern aspects of on-line testing as faced today. The contributions are largely derived from recent IEEE international on-line testing workshops.