Although dark matter comprises the vast majority of the matter in the universe, its properties remain elusive. Direct detection experiments are a promising avenue for discovering and characterizing the dark sector. These experiments seek to identify dark matter particles as they scatter off nuclei in underground detectors. The standard picture since the 1980s is that the scattering rate modulates annually due to the Earth's orbit around the Sun. We have recently discovered a new modulation effect: Unbound dark-matter particles are focused by the Sun's gravitational potential, affecting their phase-space density in the lab frame. This 'gravitational focusing' results in a significant overall shift in the phase of the annual modulation and provides a powerful new tool for characterizing the properties of the dark matter particle. Gravitational focusing has additional applications to relic neutrino searches, providing the only source of annual modulation in that case.