The Center for Matter at Atomic Pressures (CMAP) is a new National Science Foundation (NSF) Physics Frontier Center, hosted at the University of Rochester—in collaboration with researchers at MIT, Princeton, the Universities of California at Berkeley and Davis, the University at Buffalo, and the Lawrence Livermore National Laboratory (LLNL)— that focuses on understanding the physics and astrophysical implications of matter under pressures so high that the structure of individual atoms is disrupted.