The main asteroid belt (MAB), the Edgeworth-Kuiper belt (EKB), and comets belong to the main sources of dust in the Solar System. Most of Jupiter-family comets came from the EKB. Comets can be distracted due to close encounters with planets and the Sun, collisions with small bodies, a nd internal forces. We support the Eneev's idea that the largest objects in the ELB and MAB could be formed directly by the compression of rarefied dust condensations of the protoplanetary cloud but not by the accretion of small (for example, 1-km) planetesimals. The total mass of planetesimals that entered the EKB from the feeding zone of the giant planets during their accumulation could exceed tens of Earth's masses. These planetesimals increased eccentricities of 'local' trans-Neptunian objects (TNOs) and swept most of these TNOs. A small portion of such planetesimals could left beyond Neptune's orbit in highly eccentric orbits. The results of previous investigations of migration and collisional evolution of minor bodies were summarized. Mainly our recent results are presented.