The principal spectral detection algorithms developed at the Naval Research Laboratory (NRL) over the past 20 years for use in operational systems are described. These include anomaly detectors, signature-based methods, and techniques for anomalous change detection. Newer derivations are provided that have motivated more recent work. Mathematical methods facilitating the use of forward models for the prediction of spectral signature statistics are described and a detection algorithm is derived for ocean surveillance that is based on principles of clairvoyant fusion.