The evolution of star-forming regions and their thermal balance are strongly influenced by their chemical composition, which, in turn, is determined by the physicochemical processes that govern the transition between the gas phase and the solid state, specifically icy dust grains (e.g., particle adsorption and desorption). Gas-grain and grain-gas transitions as well as formation and sublimation of interstellar ices are thus essential elements of understanding astrophysical observations of cold environments (e.g., prestellar cores) where unexpected amounts of a large variety of chemical species have been observed in the gas phase. Adsorbed atoms and molecules also undergo chemical reactions that are not efficient in the gas phase. Therefore, the parametrization of the physical properties of atoms and molecules interacting with dust grain particles is clearly a key aspect to interpret astronomical observations and to build realistic and predictive astrochemical models. In this consensus evaluation, we focus on parameters controlling the thermal desorption of ices and how these determine pathways toward molecular complexity and define the location of snowlines, which ultimately influence the planet formation process. We review different crucial aspects of desorption parameters both from a theoretical and experimental points of view. We critically assess the desorption parameters (the binding energies, E_b, and the pre-exponential factor, ν) commonly used in the astrochemical community for astrophysically relevant species and provide tables with recommended values. The aim of these tables is to provide a coherent set of critically assessed desorption parameters for common use in future work. In addition, we show that a nontrivial determination of the pre-exponential factor ν using transition state theory can affect the binding energy value. The primary focus is on pure ices, but we also discuss the desorption behavior of mixed, that is, astronomically more realistic, ices. This allows discussion of segregation effects. Finally, we conclude this work by discussing the limitations of theoretical and experimental approaches currently used to determine the desorption properties with suggestions for future improvements.