Visual object recognition is often assumed to be insensitive to changes in retinal position, leading to theories and formal models incorporating position-independent object representations. However, recent behavioral and physiological evidence has questioned the extent to which object recognition is position independent. Here, we take a computational and physiological perspective to review the current behavioral literature. Although numerous studies report reduced object recognition performance with translation, even for distances as small as 0.5 degrees of visual angle, confounds in many of these studies make the results difficult to interpret. We conclude that there is little evidence to support position-independent object recognition and the precise role of position in object recognition remains unknown.