The evolution of meteor streams is controlled basically by: (a) the initial velocities with which the particles were ejected from the parent body; (b) gravitational perturbations by the planets; (c) radiation forces; and (d) collisions. This review focuses mainly on recent numerical modelling dealing with (b) and (a).Ejection velocities spread the particles around the orbit, closing the ring in a few tens of revolutions. The greater ejection velocities of smaller particles cause more rapid dispersion both around the orbit and in the cross section.A determination of the effects of gravitational perturbations must take into account the distributed properties of the stream. The stream’s evolution is dependent on the short-term impulse nature of planetary perturbations, as well as on long-term secular effects. The combined effects produce complex stream cross-sections as in the ribbon-like form of the Halley stream (Orionid and η Aquarid showers) or as in the changes in the annual position of peak shower activity shown by the Quadrantids. Perturbations may cause the orbit of a parent body to sweep rapidly across the orbit of the Earth. But the associated particle stream may not be lost as a meteor shower because it tends to become dispersed in a manner that ensures a continuing supply of particles in Earth-crossing orbits. The nodes of the observed meteoroid orbits may show very little motion compared with the rapid motion of the nodes of the orbit of the parent object.Radiation effects contribute to size separation of particles. Very small particles are blown out of the stream or spiral in toward the sun because of Poynting–Robertson drag. Older meteor streams usually show a predominance of large particles.