Detection threshold or recognition differential is defined as the signal-to-noise ratio at the beamformer output required for detection. An introduction to this topic is provided in Uricks’ Principles of Underwater Sound. The subject is frequently a source of confusion due to the multiple possible definitions of signal-to-noise ratio, the effects of nonlinearities in the signal processing, and the overall complexity of the sonar operators job of signal recognition in real-world clutter. In this paper, a review of the basic theory of mathematical relationships are provided, followed by a discussion of practical limitations in applying simple formulas to performance predictions. The relationships of detection threshold to the signal-processing approach and background-noise statistics are discussed. Active sonars in both noise and reverberation, as well as passive sonars involving energy detection, spectral analysis, and cross correlators are discussed.