Fault detection (FD) of technical processes plays an important role in improving system reliability and availability, ensuring product quality and reducing maintenance costs. It has received much attention in the past decades and found real applications in different industrial sectors. The main purpose of this habilitation thesis is to present new concepts in the fault detection of linear discrete-time systems. Part I gives a systematic introduction to the model-based FD of linear discrete time-invariant systems. In Part II and Part III, different design approaches for periodic systems and time-varying systems have been explored. Part IV takes into account the practical implementation of FD systems on computers or embedded microprocessors into account and presents FD approaches for multirate sampled-data systems and non-uniformly sampled-data systems that take into account the intersample behaviour. Due to the wide use of bus systems and wireless networks in realizing modern control systems, communication, embedded computing and control are more closely integrated. Hence, Part V handles the modelling of communication effects and the design of fault detection systems for networked control systems. Moreover, several co-design schemes of fault detection systems and communication strategies are presented as well.