A discussion of the relation between the sciences and the arts hinges on finding a common ground for the comparison of their innovative practices. It has to be a ground from which this relation can be formulated in a manner such that the involvement with the unprecedented stands in the foreground, without denying the right to being different in approach and performance. In both the sciences and the arts, what is at stake are the practices of making, an understanding of a production process with an uncertain outcome, at whose end things will stand that did not command and determine its beginning. Accordingly, the present chapter comes in two parts. The first part offers some clues for a conceptual rapprochement between the history of the sciences and the history of the arts from the perspective of a history of things in the making. The second part presents some arguments for a critical discussion of the phenomenon of “artistic research,” a concept that obviously connects to such a process view in both realms. In conclusion, the chapter offers an outlook on the potential and prospects of a “hybrid heuristics” across the arts and the sciences.