Many statistical techniques were invented in the nineteenth century by experimental scientists who personally applied their methods to authentic data sets. In these conditions the limits of what is computationally feasible are spontaneously observed. Until quite recently these limits were set by the capacity of the human calculator, equipped with pencil and paper and with such aids as the slide rule, tables of logarithms, and other convenient tables, which have been in constant use from the seventeenth century until well into the twentieth. Thus Fisher and Yates's Statistical Tables, which were first published in 1938, still contain tabulations of squares, square roots, and reciprocals, which are of great help in performing routine computations by hand. Yet by that time mechanical multiplicators, which came into fashion in the 1920s, were already quite common, as were mechanical adding machines. By 1950 addition and multiplication were combined in noisy and unwieldy desk machines driven by a small electric motor; some were capable of long division, or even of taking square roots. These improvements may have doubled or trebled the speed of computing, but they did not materially alter its scope: Until the advent of the electronic computer, the powers of the human operator set the standard. This restriction has left its mark on statistical technique, and many new developments have taken place since it was lifted. This is the theme of this introductory chapter.