Planetary systems are made up of objects with sizes ranging from gas giant planets down to asteroids and on to micron sized dust. Dust in the zodiacal cloud in the solar system originates in the break-up of asteroids and comets and then migrates in toward the Sun due to P-R drag. The dynamical evolution of the dust is also affected by the gravitational perturbations of the solar system's planets, and the consequence of those perturbations is evident in the asymmetric and clumpy structure of the zodiacal cloud. In the last couple of years features in the cloud have been identified with asteroid collisions which occurred just a few Myr ago implying that steady state models for the zodiacal cloud will have to be reconsidered. Many extrasolar systems also harbor massive dust belts and the structures of those dust belts have been linked to perturbations from unseen planets. This paper reviews the dominant physical processes affecting the evolution of dust grains and describes the techniques which have been developed to model their dynamics and identify the sources of dust structures in both the solar system and extrasolar systems.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html