Fault detection and identification (FDI) play a fundamental role in most modern industrial systems and processes. They are essential in ensuring safe and reliable operation. In this book, Chapter One and Chapter Two discuss general systems and the use of linearizations for active fault detection in nonlinear differential algebraic equations. Chapter Three provides a comparative analysis and comprehensive review of the existing fault detection methods, including manual picking and computer-aided automatic/semi-automatic extraction. Chapter Four studies self-adaptive expert systems for process monitoring and fault detection. The final chapter provides a review of an integrated Fault Detection and Diagnostics (FDD) system for HVAC and R based on virtual sensors.