In this article we explore some of the theoretical developments over the last 40 years which led to the emergence of the field of market design. This new field has had a substantive impact on policy, especially after the highly successful auctions of the mobile telephony licences in the mid-1990s in the US. The auctions replaced an inefficient allocation system where licences were allocated to applicants via a lottery and subsequently sold for large windfalls. These auctions raised substantial amount of revenue for the US government and were adopted worldwide, including in Australia. First, I provide a brief history of market design in cases where monetary payments can be used as the basis to allocate goods and services. This history starts with the game theoretical foundations of non-cooperative behaviour – as typically the interests of different individuals are in conflict, for example, when buying or selling goods and services – and then moves on to mechanism design and auction theory and practice. Second, I will review a very large experiment in Brazil where markets were created to avoid electricity rationing in 2001. The choice of this example is not inconsequential. It is meant to illustrate that such an approach to public policy can be successful even in developing countries with weaker institutions. I will then provide some concluding comments.