We review neuropsychological evidence for visual selection operating in different reference frames. There is general agreement that there may be a separation of coding space near to and farther from the body, and that deficits in selecting stimuli within each form of spatial representation may be impaired in patients with unilateral neglect. However, there remains a lack of consensus about whether all forms of spatial representation relate to the body or whether there are spatial representations based on reference frames abstracted from the body (allocentric and object-centered spatial codes). Here we will review the evidence for spatial coding in these more abstracted reference frames (allocentric and object-centered but also environmental) and argue for the psychological reality of (at least) allocentric spatial coding. We discuss computational accounts of how such codes may be created as objects are selected.