In the preceding three chapters, a host of ideas and experiments on human reasoning have been discussed, with brief accounts both of how these studies may help us explain deductive thinking, and of how the explanations have led to further experiments. In this chapter, we return to these explanations in more detail. We shall consider five main types of theory in three ways: (i) their structure and content, (ii) their successes and limits in accounting for the research data, and (iii) points on which they agree and differ. The contest between theories has been a feature of reasoning research since the early 1980s, and is still in full swing.