With much pictorial support, we review research on how vertebrate animals orient in enclosed rectilinear spaces. The phenomenon of the rotational error is introduced, along with the distinction between geometric and featural information. The circumstances under which a number of species use geometric and geatural information for relocating a target place are reviewed. Other sections examine cue competition (actually lack thereof) between geometric information and landmark cues, artificial intelligence, and the neurophysiological bases udnerlying the coding of geometric information. We then examine two theoretical issues 1) how geometry is encoded and used, 2) the modularity of mind.