This chapter traces the development and impact of signal detection theory in the study of perception. The particular emphasis will be on the extension of signal detection theory to visual perception in two-dimensional perceptual spaces, although the results presented here are general and nor restricted to the visual domain nor to the two-dimensional case. Uithin the context of the General Recognition Theory (GRT; Ashby & Townsend, 1986, see also chapters _ in this volume), we have shown that theoretical relationships exist between the unobservable notions of perceptual separability and perceptual independence and the observable (and estimable) concepts of sampling independence, marginal response invariance, and two sets of signal detection parameters (Kadlec & Townsend, 1989). These relationships and their applications will be presented here.