Psychophysics is a scientific approach to the measurement of mental processes. In Elemente der Psychophysik in 1860, Gustav Fechner defined the field, quantified Weber’s law, created a theory of judgment errors in sensory comparisons, and proposed a logarithmic law of sensation strength. In 1927, theoretical advances by Thurstone expanded the applications of psychophysical methods to stimuli not measurable on a physical scale, thereby permitting measurements of attitudes, preferences, and feelings. Stevens (1956) argued against these ideas and proposed, instead, a power law of sensation strength, an idea previously proposed by Plateau (1872). New experimental data required both camps to accommodate the influence on performance of ‘cognitive factors,’ which caused deviations from the power law of sensation. In classical psychophysical experiments, the effects of cognitive factors led to the theory of ideals, the theory of signal detection, receiver operating characteristics, and a sequential theory of psychological discrimination. At the beginning of the twenty-first century psychophysics is poised for major theoretical advances toward more refined and more extensive measurements of mental processes.