The origin of life is one of the most important but also one of the most difficult problems in science. Autocatalytic sets are believed to have played an important role in the origin of life. An autocatalytic set is a collection of molecules and the chemical reactions between them, such that the set as a whole forms a functionally closed and self-sustaining system. In this article, I present an overview of recent work on the theory of autocatalytic sets and on how this theory can be used to study the probability of emergence, the overall structure, and the further evolution of such systems, both in simple mathematical models and in real chemical systems. I also describe some (still speculative) ideas of how this theory can potentially be applied to living systems in general and perhaps even to social systems such as the economy.