The aim of this chapter is to study the history of the design and use of calculating machines to produce and use numerical tables, from the time of Babbage’s plans for difference and analytical engines to the modern digital computer, including in this analysis the role played by analog machines between the two. We will examine how the place and role of numerical tables changed throughout the different stages of this mechanization. It is our hypothesis that these processes of mechanization and, ultimately, automisation and digitalization, result in the progressive internalization of aspects of the dynamical relation between humans and tables into the machine. This chapter considers several major stages in the devising of machines for the making and use of tables, from difference engines to computers. Following these stages, we investigate how increasing demands for calculating power go hand in hand with advances in the new technological possibilities offered by machines. The way by which machines were introduced and accepted for mathematical computations will also be examined. Even though this chapter is thus structured according to the changes in the machines, the focus will be on how these changes have affected numerical tables. By doing so, it will become clear how it is not only the machine which shapes the history of the numerical table, but, also how the numerical table has impacted on the design and use of calculating machinery. In fact, as we will argue, the history of calculating machinery is reciprocal to the history of the numerical table. With the development of modern computers, in which data and programs can be manipulated in the same way, this reciprocity is expressed by an increasing interchangeability between tables and algorithms.