In this paper we argue that the data management community should devote far more effort to building data integration (DI) systems, in order to truly advance the field. Toward this goal, we make three contributions. First, we draw on our recent industrial experience to discuss the limitations of current DI systems. Second, we propose an agenda to build a new kind of DI systems to address these limitations. These systems guide users through the DI workflow, step by step. They provide tools to address the ‘pain points’ of the steps, and tools are built on top of the Python data science and Big Data ecosystem (PyData). We discuss how to foster an ecosystem of such tools within PyData, then use it to build DI systems for collaborative/cloud/crowd/lay user settings. Finally, we discuss ongoing work at Wisconsin, which suggests that these DI systems are highly promising and building them raises many interesting research challenges. Toward a System Building Agenda for Data Integration