Interaural cross-correlation-based models of binaural processing have accounted successfully for a wide variety of binaural phenomena, including binaural detection, binaural discrimination, and measures of extents of laterality based on interaural temporal disparities, interaural intensitive disparities, and their combination. This report focuses on quantitative accounts of data obtained from binaural detection experiments published over five decades. Particular emphasis is placed on stimulus contexts for which commonly used correlation-based approaches fail to provide adequate explanations of the data. One such context concerns binaural detection of signals masked by certain noises that are narrow-band and/or interaurally partially correlated. It is shown that a cross-correlation-based model that includes stages of peripheral auditory processing can, when coupled with an appropriate decision variable, account well for a wide variety of classic and recently published binaural detection data including those that have, heretofore, proven to be problematic.