This chapter provides an introduction into the field of fault detection, fault diagnosis and fault-tolerant systems with methods, which have proven their performance in practical applications. The derivation of the mathematical description of technical processes is relatively mature; however, they present challenging aspects in the fields of advanced control, supervision, fault diagnosis and fault tolerance. Effective strategies to cope with faults were considered to improve plant performance, particularly in faulty working conditions. It was also highlighted that modern plants and industrial installations can have large and flexible mechanical structures operating in uncertain environments, thus representing interesting cases for advanced control solutions. The control problem definition required the maximization or the minimization of prescribed performance objectives subject to proper system constraints, thus leading to a constrained optimization problem. The chapter also presents some closing thoughts on the key concepts discussed in the preceding chapters of this book.