This thesis describes financial markets as complex machines in the broader sense, as systems for organizing informational flows and performing certain functions in regards to the processing of transactions. We focus on the transaction infrastructure of financial markets, on the flow architecture that allows transactions to happen in the first place. First, in order for a financial market to function there needs to be some mechanism for aggregating and matching disparate transactional requests. Another mechanism is then needed in order to untangle and reduce the complexity of overlapping exposures between participants. The history of finance shows us that there are indeed certain patterns and regularities, procedures and mechanisms present in any system that processes financial transactions. The thesis describes this sequence of functions as transaction machines, understood as complex socio-technical systems for the execution of financial transactions. This is achieved by leveraging a specific philosophical account of technology coupled with a computational and evolutionary account of financial markets. We ultimately focus two types of transaction machines, performing the matching and clearing of financial flows, acting as the infrastructure of financial markets. We also provide a sketch for an evolutionary trajectory of these machines, evolving under the demands and needs of marker participants. From medieval fairs to the millisecond electronic platforms of today, transaction machines have gradually transitioned from human-based ‘hardware’ to electronic automated platforms. Moreover, we also describe the complex power dynamics of contemporary transaction machines. In as much as they are the dominant hubs of global financial markets, the thesis argues for the necessity of a more granular account of the functioning and evolution of transaction machines.