In January 2019, the US Department of Energy, Office of Science program in Advanced Scientific Computing Research, convened a workshop to identify priority research directions (PRDs) for in situ data management (ISDM). A fundamental finding of this workshop is that the methodologies used to manage data among a variety of tasks in situ can be used to facilitate scientific discovery from many different data sources—simulation, experiment, and sensors, for example—and that being able to do so at numerous computing scales will benefit real-time decision-making, design optimization, and data-driven scientific discovery. This article describes six PRDs identified by the workshop, which highlight the components and capabilities needed for ISDM to be successful for a wide variety of applications—making ISDM capabilities more pervasive, controllable, composable, and transparent, with a focus on greater coordination with the software stack and a diversity of fundamentally new data algorithms.