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...