Our Sun is known to be immersed in an extended ethereal dust cloud
produced and continuously replenished by small bodies - comets,
asteroids, and Kuiper Belt Objects. Similarly, other main-sequence stars
can harbor non-primordial dust disks maintained by invisible small
bodies (comets, planetesimals). By now, many of these circumstellar
disks have been detected and some imaged with modern observational
techniques. We start with an overview of current observational knowledge
about the disks, including disk dimensions and geometry, dust properties,
gas contents, dependence of disk properties on the stellar age. We then
outline main physical mechanisms acting in such disks. First we consider
an "unperturbed" disk (ignoring a possible planet inside) to show
that destructive collisions between constituent particles together with
radiation pressure forces are largely responsible for setting up size
distributions of grains. Next, the interaction of a dust disk with
embedded planets is considered. Secular and resonant perturbations as
well as close encounters of dust grains with an alleged planet would
induce a variety of features (warps, inner gaps, voids, clumps, etc.) in
the disk. These can be directly observed, which offers an indirect
method to search for extrasolar planets. To summarize, disks around
main-sequence stars: are common observational phenomena; appear
naturally in the context of planetary system formation theories; can be
used as tracers of planets, small bodies, and circumstellar environments;
may act as a source of interstellar material.