Scientific user facilities - particle accelerators, telescopes, colliders, supercomputers, light sources, sequencing facilities, and more - operated by the U.S. Department of Energy (DOE) Office of Science (SC) generate ever increasing volumes of data at unprecedented rates from experiments, observations, and simulations. At the same time there is a growing community of experimentalists that require real-time data analysis feedback, to enable them to steer their complex experimental instruments to optimized scientific outcomes and new discoveries. Recent efforts in DOE-SC have focused on articulating the data-centric challenges and opportunities facing these science communities. Key challenges include difficulties coping with data size, rate, and complexity in the context of both real-time and post-experiment data analysis and interpretation. Solutions will require algorithmic and mathematical advances, as well as hardware and software infrastructures that adequately support data-intensive scientific workloads. This paper presents the summary findings of a workshop held by DOE-SC in September 2015, convened to identify the major challenges and the research that is needed to meet those challenges.