The continued evolution of money has profound implications for the economic and power relationships among individuals, businesses, and governments, particularly concerning questions of custody, privacy, and accountability. The UCL Future of Money Initiative delivers a line of research, education, and public engagement activities concerning the socio-technical systems that form the basis for payments in the modern world, including the roles of directly held property and custodians within that system, as well as the past and future evolution of the mechanisms by which private individuals and businesses exchange value for goods and services. We investigate the use of accounts in the execution of retail transactions, as well as the emergence of digital assets featuring various models for ownership, possession, and control, as characteristics of the evolving payments landscape in the digital economy. Our research initiative provides a platform to explore and analyse existing and proposed systems for the transaction of value, and to propose new systems that deliver the best outcomes for the people they serve.