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This report documents the program and the outcomes of Dagstuhl Seminar 19491 "Big Graph Processing Systems". We are just beginning to understand the role graph processing could play in our society. Data is not just getting bigger, but, crucially, also more connected. Exploring, describing, predicting, and explaining real- and digital-world phenomena is increasingly relying on abstractions that can express interconnectedness. Graphs are such an abstraction. They can model naturally the complex relationships, interactions, and interdependencies between objects. However, after initial success, graph processing systems are struggling to cope with the new scale, diversity, and other real-world needs. The Dagstuhl Seminar 19491 aims to addresses the question: How could the next decade look like for graph processing systems? To identify the opportunities and challenges of graph processing systems over the next decade, we met in December 2019 with circa 40 high-quality and diverse researchers for the Dagstuhl Seminar on Big Graph Processing Systems. A main strength of this seminar is the combination of the data management and large-scale systems communities. The seminar was successful, and addressed in particular topics around graph processing systems: ecosystems, abstractions and other fundamental theory, and performance.