With the growing use of magnetic nanoparticles in biological systems and magnetic nanostructures in information storage and low-power computation, studies of the small-scale behavior of tiny magnets and their interfaces with other materials have become essential for global challenges in health and sustainability. For example, new magnetic systems may permit single-molecule nuclear magnetic resonance directly through magnetic sensing. This symposium brings together prominent researchers from around the world who are pioneering approaches to probe the foundations of nanoscale magnetism. The smallest length scale envisioned is the atomic scale, where the chemical sensitivity of X-rays can now be combined with the atomic-scale resolution of scanning tunneling microscopes. The largest scale is that of fundamental excitations of magnetic systems, i.e., the vortex scale, where scanning magnetic probes have now visualized a single vortex and probed its pinning dynamics from a single site that pins it in place. In between, the use of exceptionally sensitive, scanning, quantum-coherent probes of magnetic fields can pick up the magnetic field of a few protons in a molecule, or detect the fields of nearby molecules while optically trapped in a biological fluid. The advances in these techniques suggest many problems in physics, biology, and chemistry can now be solved by direct measurement of nanoscale magnetism.