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The purpose of this article is to review and evaluate the range of theories proposed to explain findings on the use of geometry in reorientation. We consider five key approaches and models associated with them and, in the course of reviewing each approach, five key issues. First, we take up modularity theory itself, as recently revised by Lee and Spelke (Cognitive Psychology, 61, 152-176, 2010a; Experimental Brain Research, 206, 179-188, 2010b). In this context, we discuss issues concerning the basic distinction between geometry and features. Second, we review the view-matching approach (Stürzl, Cheung, Cheng, &amp; Zeil, Journal of Experimental Psychology: Animal Behavior Processes, 34, 1-14, 2008). In this context, we highlight the possibility of cross-species differences, as well as commonalities. Third, we review an associative theory (Miller &amp; Shettleworth, Journal of Experimental Psychology: Animal Behavior Processes, 33, 191-212, 2007; Journal of Experimental Psychology: Animal Behavior Processes, 34, 419-422, 2008). In this context, we focus on phenomena of cue competition. Fourth, we take up adaptive combination theory (Newcombe &amp; Huttenlocher, 2006). In this context, we focus on discussing development and the effects of experience. Fifth, we examine various neurally based approaches, including frameworks proposed by Doeller and Burgess (Proceedings of the National Academy of Sciences of the United States of America, 105, 5909-5914, 2008; Doeller, King, &amp; Burgess, Proceedings of the National Academy of Sciences of the United States of America, 105, 5915-5920, 2008) and by Sheynikhovich, Chavarriaga, Strösslin, Arleo, and Gerstner (Psychological Review, 116, 540-566, 2009). In this context, we examine the issue of the neural substrates of spatial navigation. We conclude that none of these approaches can account for all of the known phenomena concerning the use of geometry in reorientation and clarify what the challenges are for each approach.

25 years of research on the use of geometry in spatial reorientation: a current theoretical perspective