In the transition to a society with net-zero carbon emissions, high penetration of distributed renewable power generation and large-scale electrification of transportation and heat are driving the conventional distribution network operators (DNOs) to evolve into distribution system operators (DSOs) that manage distribution networks in a more active and flexible way. As a radical decentralized data management technology, distributed ledger technology (DLT) has the potential to support a trustworthy digital infrastructure facilitating the DNO–DSO transition. Based on a comprehensive review of worldwide research and practice, as well as the engagement of relevant industrial experts, the application of DLT in distribution networks is identified and analyzed in this article. The DLT features and DSO needs are first summarized, and the mapping relationship between them is identified. Detailed DSO functions are identified and classified into five categories (i.e., “planning,” “operation,” “market,” “asset,” and “connection”) with the potential of applying DLT to various DSO functions assessed. Finally, the development of seven key DSO functions with high DLT potential is analyzed and discussed from the technical, legal, and social perspectives, including peer-to-peer energy trading, flexibility market facilitation, electric vehicle charging, network pricing, distributed generation register, data access, and investment planning.