The International Conference on Cognitive Modeling brings together researchers who develop computational models to explain and predict cognitive data. The core theme of the 2004 conference was Integrating Computational Models, encompassing an integration of diverse data through models of coherent phenomena; integration across modeling approaches; and integration of teaching and modeling. This text presents the proceedings of that conference. The International Conference on Cognitive Modeling 2004 sought to grow the discipline of computational cognitive modeling by providing a sophisticated modeling audience for cutting-edge researchers, in addition to offering a forum for integrating insights across alternative modeling approaches in both basic research and applied settings, and a venue for planning the future growth of the discipline. The meeting included a careful peer-review process of 6-page paper submissions; poster-abstracts to include late-breaking work in the area; prizes for best papers; a doctoral consortium; and competitive modeling symposia that compare and contrast different approaches to the same phenomena.