According to the shoving model the non-Arrhenius temperature dependence of supercooled liquids' relaxation time (or viscosity) derives from the fact that the high-frequency shear modulus is temperature dependent in the supercooled phase, often increasing a factor of three or four in the temperature interval over which the relaxation time increases by ten to fifteen decades. In this paper we have compiled all tests of the shoving model known to us. These involve rheological data obtained by different techniques, high-frequency sound-wave data, neutron scattering data for the vibrational mean-square displacement, data obtained at or below the glass transition, as well as data testing the model under out-of-equilibrium conditions, i.e., during aging. Most data confirm the model, some do not. We conclude that more work is needed to precisely characterize the model's range of applicability.