The sublimation and condensation of ices play a very important role in the formation of planetary systems, in the evolution of some solar system bodies as well as in the equilibrium and matter exchanges between surface and atmosphere of most planets and satellites. The precise knowledge of vapour pressure of molecular solids at all relevant temperatures is mandatory, but the published sublimation relations are not always accurate enough. All published experimental measurements, and empirical and thermodynamical relations for the vapour pressure of 53 different species in their pure solid phases are reviewed. For several species, we also calculate the vapour pressure with accurate thermodynamic formulae from the triple point down to low temperatures. For 27 species (H2O, O2, O3, CO, CO2, CH3OH, HCOOH, CH4, C2H2, C2H4, C2H6, C6H6, HCN, HC3N, C2N2, C4N2, N2, NH3, NO, N2O, H2S, SO2, AsH3, Ne, Ar, Kr, and Xe) we are able to propose vapour pressure relations, either empirical or theoretical, valid over a large range of temperatures, representative of astrophysical environments. All these relations are more accurate than those currently used in the astrophysical literature. In particular, most of the relations commonly used in the astrophysical literature are based on the data reported by Lide (2006) in the CRC Handbook of Chemistry and Physics, which are inaccurate for several compounds. The most problematic case is CO ice, for which a sublimation relation extrapolated from the liquid–gas equilibrium (Fanale and Salvail, 1990) is used in most of the models simulating the activity of comet nuclei.