The increased complexity of modern systems necessitates automated anomaly detection methods to detect possible anomalous behavior determined by malfunctions or external attacks. We present formal methods for inferring (via supervised learning) and detecting (via unsupervised learning) anomalous behavior. Our procedures use data to construct a signal temporal logic (STL) formula that describes normal system behavior. This logic can be used to formulate properties such as “If the train brakes within 500 m of the platform at a speed of 50 km/hr, then it will stop in at least 30 s and at most 50 s.” Our procedure infers not only the physical parameters involved in the formula (e.g., 500 m in the example above) but also its logical structure. STL gives a more human-readable representation of behavior than classifiers represented as surfaces in high-dimensional feature spaces. The learned formula enables us to perform early detection by using monitoring techniques and anomaly mitigation by using formal synthesis techniques. We demonstrate the power of our methods with examples of naval surveillance and a train braking system.