The institution of money can be seen as a foundational social mechanism providing communities with the ability to quantify the results of economic processes and collectively regulate independent activities of production and trade – money can be said, indeed, to constitute the micro-macro link in economics. As such, investigations of money’s role in the economy can be fruitfully combined with the methods of computational social science. This paper revisits the major positions taken in the contested landscape of monetary theory, evaluating seminal contributions under the light of the current literature on emergence, coordination and agent-based modeling. We start out by presenting a comparative review of the way different intellectual traditions in mainstream economics, heterodox economics, and economic sociology attempt to specify the nature of money as an institution and clarify its role in the economy. We pay especially close attention to the contrast between the sociology of money (including classical references in Simmel, Polanyi, and Giddens, but also more recent debates centered around Geoffrey Ingham, Heiner Ganßmann and monetary institutionalism) and the “microfoundations” tradition prevalent in economics (with emphasis on “money as memory” approaches and on coordination/reciprocity games). We then propose a simplified agent-based framework, including agent specification, matching routines, trading strategies and topology, that can serve as a starting point for an investigation of money that takes stock of economic sociology’s critique of mainstream theories of money. This is envisioned as a toolkit that can be adapted to different research questions and is designed in a way that is sensitive to the several potential purposes of specific models, to the challenges that equifinality and design choices pose to abstract or theoretical modeling, and to the need for explicit specification of the concept of “emergence” in the study of monetary institutions. We conclude by indicating different potential implementations of this framework to illuminate research gaps that a sociological perspective identifies in the theoretical money modeling literature, namely: i. money’s role in the formation of economic structure, ii. convergence to common forms of quantification, iii. interdependence and systemic instability, iv. bootstrapping and self-reference, v. the relationship between monetary forms and productive processes, vi. coordination through value and vii. monetary plurality. Summing up the above, we propose a concept of money as a form of belonging to economic complexity, an approach that cuts across disciplinary divides in monetary theory and that we believe could inform further research in the field of money studies.