More than 20% of nearby main sequence stars are surrounded by debris disks, where planetesimals, larger bodies similar to asteroids and comets in our own Solar System, are ground down through collisions. Debris disks represent the end-stage of circumstellar disk evolution, composed of remnant material that provides a fossil record of earlier planet formation processes. Planets orbiting within these disks sculpt the dust through gravitational interactions, producing observable structures that illuminate the dynamical evolution of the system. I will highlight recent results from the Atacama Large Millimeter/submillimeter Array (ALMA), which reveal a wealth of asymmetric structure in nearby debris disks. Modeling work is helping us understand the dynamical origin of these structures and potentially connect them to unseen planets.