Current understanding of the formation of circumstellar discs as a natural accompaniment to the process of low-mass star formation is briefly reviewed. Models of the thermal emission from the dust discs around the prototype stars $\alpha $ Lyr, $\alpha $ PsA, $\beta $ Pic and $\varepsilon $ Eri are discussed, which indicate that the central regions of three of these discs are almost devoid of dust within radii ranging between 17 and 26 AU, with the temperature of the hottest dust lying between about 115 and 210 K. One possible explanation of the dust-free zones is the presence of a planet at the inner boundary of each cloud that sweeps up grains crossing its orbit. The discs have outer radii that range between about 250 and 800 AU and have dust masses that are unlikely to exceed about 300 Earth masses. Assuming a gas: dust ratio of 100:1 for the pre-main-sequence disc this corresponds to a mass of ca. 0.1 [Note: Equation omitted. See the image of page 33 for this equation.] comparable to that of the pre-main-sequence star HL Tau. The colour, diameter and thickness of the optical image of $\beta $ Pic, obtained by coronagraphic techniques, have provided further information on the size, radial distribution of number density and orbital inclination of the grains. The difference in surface brightness on the two sides of the disc is puzzling, but might be explained if the grains are elongated and aligned by the combined effects of a stellar wind and a magnetic field of spiral configuration. Finally, we discuss the orbital evolution and lifetimes of particles in these discs, which are governed primarily by radiation pressure, Poynting--Robertson drag and grain--grain collisions. Although replenishment of these discs may be occurring, for example by grains ejected from comets, discs of initial radius ca. 1000 AU can survive Poynting--Robertson depletion over the stellar age and there is no prima facie evidence as yet in favour of a balance between sources and sinks of dust.