The paper presents a unified approach and general solution of the robustness problem in fault detection and isolation concepts. The ultimate objective is the design of an unknown input fault-detection observer providing a perfect decoupling between unknown inputs and faults. If this is not possible because certain prerequisites are not fulfilled, two optimal compromises in the time domain and in the frequency domain are described. The basic definitions concerning robustness and unknown input fault detectability are given, and the design techniques for the proposed approaches are outlined. The cross-connections to other methods are discussed and a practical example is given.