Geophysical remote-sensing methods, particularly seismology, provide an incredibly detailed view of the structure and composition of Earth’s mantle. The seismic velocity structure of the deep mantle can be used, in theory, to constrain its temperature, mineralogy and composition. However, inversion of the mantle velocity structure relies on quantitative knowledge of the elastic properties of Earth’s mantle minerals. Knowledge of the elastic properties of mantle minerals is primarily derived from experimental in situ measurements of sound-wave velocities at high pressure and temperature. In this Technical Review, we highlight the major methodologies that are used to constrain the elastic properties of deep-mantle minerals and discuss their advantages, limitations and future potential. We focus on light-scattering techniques in the diamond-anvil-cell and ultrasonic methods in large-volume presses, which have provided the majority of elasticity data on deep-mantle minerals to date and will likely continue to do so in the foreseeable future. We summarize the current state of knowledge with respect to the elastic properties of typical minerals in the mantle transition zone and lower mantle, where substantial advances have recently been made, and highlight major gaps in the published data.