This article aims at introducing the concept of manipulative abduction, by showing how we can find at various levels of cognitive activity various methods of manipulative constructivity. From this perspective, also creativity and discovery are no longer seen as mysterious irrational processes, but, thanks to constructive accounts, they are viewed as complex relationships among different inferential steps that can be clearly analyzed and identified. I maintain that the analysis of the blending of external and class="EmphasisTypeItalic ">internal representations and of what I have called epistemic mediators is important not only to delineate the actual practice of manipulative abduction but also to further enhance the development of programs computationally adequate in rediscovering or discovering for the first time, for example, scientific hypotheses or mathematical theorems and to favor the design of more realistic and efficient robots. I will focus on those particular kinds of abductive cognition that resort to the existence of extra-theoretical ways of thinking – thinking through doing – centering the attention to the fact that many cognitive processes are centered on "external representations," as a means to create communicable accounts of new experiences ready to be integrated into previously existing systems of experimental and theoretical practices.