The World Wide Web has emerged as the middleware of choice for most distributed systems. Recent standardization efforts for the Web of Things and Linked Data are now turning hypermedia into a homogeneous information fabric that interconnects everything-devices, information resources, abstract concepts, etc. The latest standards allow clients not only to browse and query, but also to observe and act on this hypermedia fabric. Researchers and practitioners are already looking for means to build more sophisticated clients able to meet their design objectives through flexible autonomous use of this hypermedia fabric. Such autonomous agents have been studied to large extent in research on distributed artificial intelligence and, in particular, multi-agent systems. These recent developments thus motivate the need for a broader perspective that can only be achieved through a concerted effort of the research communities on the Web Architecture and the Web of Things, Semantic Web and Linked Data, and Autonomous Agents and Multi-Agent Systems. The Dagstuhl Seminar 21072 on "Autonomous Agents on the Web" brought together leading scholars and practitioners across these research areas in order to support the transfer of knowledge and results-and to discuss new opportunities for research on Web-based autonomous systems. This report documents the seminar's program and outcomes.