The pragmatist philosopher Peirce insisted that besides deduction and induction there is a third main form of inference, abduction, which is the only type of inference capable of producing new ideas. Also he defined abduction as a stage of the methodological process in science, where hypotheses are formed to explain anomalies. Basing on these seminal ideas, scholars have proposed modified, widened or alternative definitions of abduction and devised taxonomies of abductive inferences. Influenced by Peirce's seminal writings and subsequent treatments on abduction in philosophy of science, design scholars have in the last 40 years endeavoured to shed light on design by means of the concept of abduction. The first treatment was provided by March in 1976. He viewed that abduction, which he called "productive reasoning", is the key mode of reasoning in design. He also presented a three-step cyclic design process, similar to Peirce's methodological process in science. Among the many other later treatments of design abduction, Roozenburg's definition of explanatory and innovative abduction is noteworthy. However, an evaluation of the related literature suggests that research into abduction in design is still in an undeveloped stage. This research shows gaps in coverage, lack of depth and diverging outcomes. By focusing on the differences between science and design as well as on empirical knowledge of different phenomena comprising design, new conceptions of abduction in design are derived. Given the differences of context, abduction in design shows characteristics not yet found or identified in science. For example, abduction can occur in connection to practically all inference types in design; it is a property of an inference besides an inference itself. A number of the most important abductive inference types as they occur in design are identified and discussed in more detail.