This paper presents an overview of a learning methodology for detecting and diagnosing faults in nonlinear dynamic systems. The main idea behind this approach is to monitor the plant for any off-nominal behavior due to faults utilizing on-line approximators. In the presence of a failure, the on-line approximator can be used as an estimate of the nonlinear fault function for fault diagnosis purposes. Furthermore, during the initial stage of monitoring, the learning capabilities of the on-line approximator can be used to learn the modeling errors, thereby enhancing the robustness properties of the fault diagnosis scheme.