We described a historical development of signal detection theory from fundamental works by Neyman and Pearson to the receiver operating characteristic curve. We compared the U.S. Environmental Protection Agency regulatory method detection limit and the detection limit, as well as the International Organization for Standardization decision level for radionuclides, with the Currie critical level and the detection limit. The latter is also referred to as the minimum detectable activity. Among these concepts, the critical level is used for censoring: detected or not detected. If an analyte is not detected, an upper limit is set. The signal detection theory approach can be generalized to three regions—not detected, detected, and undecided—based on data objectives criteria and not necessarily on statistical criteria. Data objectives for an analytical result can be derived, for instance, from risk assessment. The complexity of mathematical treatment depends on the choice of the probability density function, and it is relatively simple for Gaussian statistics. We provided numerical examples illustrating the performance of several signal detection theory methods as well as a direct application to radiation measurements.