It is the aim of this chapter to evaluate the role of (modern) computing as a mathematical technology: how do the histories of computing and mathematics intertwine (or not) and what does this tell us about (the history of) mathematics itself and how it is perceived today? Of course, it is not possible within the scope of one chapter to tell the complete histories and so the focus here will be on overall developments in the 20th and early 21st century of a (changing) relation between, on the one hand, mathematics – its practice, its self-perception and its results – and, on the other, computational technologies and the academic fields which are anchored in it historically. That history is very broad. In order to give focus in this chapter, I will concentrate mainly on the U.S. It should be emphasized here that this does not mean that there are no interesting histories to write in relation to other national and cultural contexts and their relations to the U.S. (see for instance, (Gerovich 2002) for Russia and (Mounier-Kuhn 2011) for France). The chapter will develop along four major topics: the early history of computers in relation to mathematics; the use of computational technology within mathematics; mathematics as a tool for computation and, finally, the changing disciplinary identity of mathematics from the perspective of computational technologies.