  (abridged) This review is based on an extensive work done in collaboration
with N. Gorkavyi, J. Mather, and T. Taidakova, which aimed at the physical
modelling of the interplanetary dust (IPD) cloud in the Solar system, i.e.,
establishing a link between the observable characteristics of the zodiacal
cloud and the dynamical and physical properties of the parent minor bodies. Our
computational approach permits with modest computer resources to integrate the
trajectories of hundreds of particles and to effectively store up to
$10^{10-11}$ positions, which provides a high fidelity 3D distribution of the
dust. Our numerical codes account for the major dynamical effects that govern
the motion of IPD particles. We have demonstrated the efficacy of our codes by
performing the following analyses: (i) simulation of the distribution of
Centaurs (comets scattered in their journey from the Kuiper belt inward the
Solar system) and revealing the effects of the outer planets in producing
`cometary belts'; (ii) detailed inspection of a rich resonant structure found
in these belts, which predicts the existence of gaps similar to the Kirkwood
gaps in the main asteroid belt; (iii) a preliminary 3-D physical model of the
IPD cloud, which includes three dust components -- asteroidal, cometary, and
kuiperoidal -- and is consistent with the available data of Pioneers and
Voyagers dust detectors; (iv) modeling of the IPD cloud, which provides a
zodiacal light distribution in accord, to the order of 1%, with a subset of the
COBE/DIRBE observations; and (v) showing that the resonant structure in dusty
circumstellar disks of Vega and Epsilon Eridani is a signature of embedded
extrasolar planets. Further improvements of our modelling and their importance
for astronomy and cosmology are outlined.
