This dissertation aims at elucidating the history of Vernon Smith's experimental economics by focusing its attention upon the three themes of rationality, minds and machines that assumed significance at different (albeit overlapping) stages of the development of Smith's experimental economics with the help of his published and unpublished papers. Chapter 1 is devoted to the scrutiny of the form of rationality incorporated into the portions of Smith's laboratory experiments whose results have usually been taken as corroborations of his 'Hayek Hypothesis.' By bringing into the foreground Smith's definite position on demand theory and its concrete instantiations on many different occasions, we make the case that Smith has consistently imposed by means of the induced value theory certain narrowly defined preference structures that have definite implications for the form of rationality instantiated in the laboratory. The main narrative in Chapter 2 concerns Smith's intellectual interchanges with behavioral scientists in the early 1960s, more specifically, his reactions to behavioral scientists' attempts at cognitive modeling. We present several reasons for interpreting Smith's initiation of the attempt at the maximization-based induced value theory as an endeavor to discipline subjects' minds. We also provide in Chapter 2 a portrayal of Smith's missed opportunities to get involved in the large-scale laboratory experimentation projects pursued in the 1950s in close connection with several branches of psychology. Chapter 3 consists of two parts. In Part 1, we describe the origin of mechanism design economics, and offer a detailed explanation of the analytical kinship between Smith's 'microeconomic system theory' and the standard theoretical framework utilized in mechanism design economics. Part 2 is devoted to describing the roles played by the computer in both Smith's empirical research agenda and the theoretical, mechanism design research pursued by Stanley Reiter (one of Smith's intellectual companions since the 1950s). Our historical narrative in Chapter 3 is intended to clarify that computer experience and computational theory drove the development of Reiter' version of mechanism design economics, and that they also (partially) shaped some crucial events in the history of Smith's version of experimental economics.