Signal detection theory is a framework developed in mathematical psychology to explain judgement with perceptual uncertainty, and is used in a variety of fields of psychonomics. It quantifies signal detectability, which is the ability to detect a perceived signal, and response bias, which is the tendency to overestimate or underestimate the existence of a signal. It is essential for applied researchers to understand its mathematical background and theoretical development to date in order to apply the theory properly and productively. However, few comprehensive documents are available that comprehensively describe the theory in Japanese. Therefore, this paper addresses the basic concepts and methods of the theory with related mathematical backgrounds and reviews its recent theoretical developments.