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This report documents the program and the outcomes of Dagstuhl Seminar 25171, "Holistic Graph-Processing Systems: Enabling Real-World Scale and Societal Impact". Motivated by the need to tackle the challenges that massive and complex data production and consumption bring to our interconnected, digital world, this seminar focused on large-scale graph processing as a systematic approach to transform these challenges into opportunities. Graphs provide a universal mathematical abstraction for such data, and they already influence various sectors - such as logistics, drug discovery, or fraud detection. However, we have only begun to realize their potential. Nevertheless, the benefits of graph processing could be canceled out by the rapid increase in data scale and diversity, as well as the increasing complexity in developing, executing, and sharing graph-based algorithms and workflows. The emerging field of graph processing systems promises to tackle these challenges. To make such systems effective and efficient, and facilitate their adoption, we need holistic approaches to cope with data transformation and ingestion, workload and system dynamics, high-tier graph programming and co-design with the platform, the emerging computing continuum, and domain-specific needs, among others. Our seminar explored the symbiosis of graph systems, machine learning, and network science by bringing together researchers, developers, and practitioners actively working on these topics with a focus on graphs. The seminar featured a mix of invited talks, expert panels, and focused discussion groups. The report documents these different elements, summarizes the main findings, and identifies the open problems and challenges that we will tackle next as a joint community.