In the last decade considerable research efforts have been spent to seek for systematic approaches to Fault Diagnosis (FD) in dynamical systems. Special attention has been put in robotic systems, especially for those operating in remote or hazardous environments, where a high degree of safety as well as self-diagnostics capabilities are required. On the other hand, the development of effective strategies of fault diagnosis for robot manipulators operating in an industrial context is a critical research task. Several FD techniques for robot manipulators have been proposed in the literature, although the problem of their application to industrial robots has not been extensively investigated. In this chapter different discretetime observer-bas...