Abstract For the improvement of reliability, safety and efficiency advanced methods of supervision, fault-detection and fault diagnosis become increasingly important for many technical processes. This holds especially for safety related processes like aircraft, trains, automobiles, power plants and chemical plants. The classical approaches are limit or trend checking of some measurable output variables. Because they do not give a deeper insight and usually do not allow a fault diagnosis, model-based methods of fault-detection were developed by using input and output signals and applying dynamic process models. These methods are based, e.g., on parameter estimation, parity equations or state observers. Also signal model approaches were developed. The goal is to generate several symptoms indicating the difference between nominal and faulty status. Based on different symptoms fault diagnosis procedures follow, determining the fault by applying classification or inference methods. This contribution gives a short introduction into the field and shows some applications for an actuator, a passenger car and a combustion engine.