Main sequence stars, like the Sun, are often found to be orbited by circumstellar material that can be categorized into two groups, planets and debris. The latter is made up of asteroids and comets, as well as the dust and gas derived from them, which makes debris disks observable in thermal emission or scattered light. These disks may persist over Gyrs through steady-state evolution and/or may also experience sporadic stirring and major collisional breakups, rendering them atypically bright for brief periods of time. Most interestingly, they provide direct evidence that the physical processes (whatever they may be) that act to build large oligarchs from micron-sized dust grains in protoplanetary disks have been successful in a given system, at least to the extent of building up a significant planetesimal population comparable to that seen in the Solar System’s asteroid and Kuiper belts. Such systems are prime candidates to host even larger planetary bodies as well. The recent growth in interest in debris disks has been driven by observational work that has provided statistics, resolved images, detection of gas in debris disks, and discoveries of new classes of objects. The interpretation of this vast and expanding dataset has necessitated significant advances in debris disk theory, notably in the physics of dust produced in collisional cascades and in the interaction of debris with planets. Application of this theory has led to the realization that such observations provide a powerful diagnostic that can be used not only to refine our understanding of debris disk physics, but also to challenge our understanding of how planetary systems form and evolve.