There is a long history of research into depth percepts from very large disparities, beyond the fusion limit. Such diplopic stimuli have repeatedly been shown to provide reliable depth percepts. A number of researchers have pointed to differences between the processing of small and large disparities, arguing that they are subserved by distinct neural mechanisms. Other studies have pointed to a dichotomy between the processing of 1st- and 2nd-order stimuli. Here we review literature on the full range of disparity processing to determine how well different proposed dichotomies map onto one another, and to identify unresolved issues.