Creativity is typically defined as the generation of novel and useful ideas or artifacts. This generative capacity is crucial to everyday problem solving, technological innovation, scientific discovery, and the arts. A central concern of cognitive scientists is to understand the processes that underlie human creative thinking. We review evidence that one process contributing to human creativity is the ability to generate novel representations of unfamiliar situations by completing a partially specified relation or an analogy. In particular, cognitive tasks that trigger generation of relational similarities between dissimilar situations -- distant analogies -- foster a kind of creative mind-set. We discuss possible computational mechanisms that might enable relation-driven generation, and hence may contribute to human creativity, and conclude with suggested directions for future research.