Models of stereopsis have focused on developing strategies for identifying common features in the 2 half-images so that disparity may be computed. This emphasis ignores the unpairable features that arise at occluding contours (half-occlusions). Most models treat half-occlusions as noise or outliers that are interpreted after disparity processing is completed. A series of experiments reveal that occlusion relationships are sensed during the earliest stages of binocular processing. The authors hypothesize the existence of receptive field structures that sense the local structure of stereoscopic occlusion relationships to account for these findings. Finally, a simple theoretical framework is presented in which fusion, stereopsis, and occlusion are unified. This theory explains the co-occurrence of stereopsis and diplopia and how half-occlusions escape the suppression characteristic of binocular rivalry.