This review is based on extensive work done in collaboration with N. Gorkavyi, J. Mather, and T. Taidakova, which aimed at physical modeling 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 one to integrate the trajectories of hundreds of particles and to effectively store up to 1010–11 positions with modest computer resources, providing a high fidelity 3D distribution of the dust. Our numerical codes account for the major dynamical effects that govern the motion of IPD particles: Poynting-Robertson (P-R) drag and solar wind drag; solar radiation pressure; particle evaporation; gravitational scattering by the planets; and the influence of mean-motion resonances. The incorporation of secular resonances and collisions of dust particles (both mutual and with interstellar dust) is underway. 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 in 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 Pioneer and Voyager 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 modeling and their importance for astronomy and cosmology are outlined.