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Analogical reasoning appears to play a key role in creative design. In briefly reviewing recent research on analogy-based creative design, this article first examines characterizations of creative design and then analyzes theories of analogical design in terms of four questions: why, what, how and when? After briefly describing recent AI theories of analogy-based creative design, the article focuses on three theories instantiated in operational computer programs: Syn, DSSUA (Design Support System Using Analogy) and Ideal. From this emerges a related set of research issues in analogy-based creative design. The main goal is to sketch the core issues, themes and directions in building such theories.