The Atacama Large Aperture Submillimeter Telescope (AtLAST) is a concept for a 50m class single-dish telescope that will provide high sensitivity, fast mapping of the (sub-)millimeter sky. Expected to be powered by renewable energy sources, and to be constructed in the Atacama desert in the 2030s, AtLAST’s suite of up to six state of-the-art instruments will take advantage of its large field of view and high throughput to deliver efficient continuum and spectroscopic observations of the faint, large-scale emission that eludes current facilities. The AtLAST design study project is currently supported by a Horizon 2020 grant aimed at studying the governance, telescope design, site selection, telescope operations, sustainable energy supply, and science drivers of the future AtLAST observatory. With quantified and specific science goals, we can begin to place technical specifications on the telescope and its instrumentation. As a first step in this process, we conducted a consultation on potential AtLAST science with the global (sub-)millimeter astrophysics community. The consultation involved nearly 100 scientists based in 22 countries, and the resulting 28 use cases indicate the breadth of transformational science that such a high-throughput facility could make possible: from exploring the prebiotic molecular chemistry of comets in our own Solar System, detecting the extended, diffuse cold gas in the circumgalactic medium of both our own and distant galaxies, to detailed measurements of the thermal, kinetic, and relativistic Sunyaev-Zeldovich effect and mapping of large-scale structure. Already these science cases define some core requirements for AtLAST’s instrumentation: wide bandwidths, multichroic observations, high spectral resolution, fast mapping and a large field of view. Further refinement of these is planned over the course of the current EU-funded project, resulting in detailed case studies of the telescope and instrumentation requirements needed by the community to deliver a next-generation submillimeter observing facility.