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. On-Line Testing for VLSI 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. Guest editors Michael Nicolaidis, Yervant Zorian and Dhiraj Pradhan organized the articles into six chapters. In the first chapter the editors introduce a large number of approaches with an expanded bibliography in which some references date back to the sixties. On-Line Testing for VLSI is an edited volume of original research comprising invited contributions by leading researchers.