The presentation summarizes geophysical models for Precambrian cratons, including the structure of the crust and the lithospheric mantle. A particular focus is on thermo-compositional heterogeneity of the lithospheric mantle as constrained by different geophysical data sets: (i) thermal structure of the Precambrian lithosphere based on surface heat flow data, (ii) non-thermal part of upper mantle seismic velocity heterogeneity based on a joint analysis of thermal and seismic tomography data, and (iii) lithosphere density heterogeneity as constrained by free-board and satellite gravity data. The latter is compared with xenolith data from the Siberian kimberlite provinces. An analysis of surface heat flow indicates that many Precambrian cratons (particularly the cratons of Laurasia) are characterized by extremely low surface heat flow (<25-30 mW/m2), which is in apparent contradiction with a worldwide compilation of cratonic xenolith P-T arrays, which are usually consistent with surface heat flow of around 40 mW/m2. In regions with very low heat flow, the depth extent of the lithospheric keels locally may reach the depth of 300-350 km. In contrast, the lithosphere of the cratons which were a part of the Gondwanaland does not presently exceed 250 km depth. An analysis of temperature-corrected seismic velocity structure indicates strong vertical and lateral heterogeneity of the cratonic lithospheric mantle, with a pronounced stratification in many Precambrian terranes; the latter is supported by xenolith data from the Slave craton and the Baltic Shield. The lateral extent of depleted lithospheric keels diminishes with depth and, below a 150-200 km depth, is significantly smaller than geological boundaries of the cratons. A comparison of density structure of the cratonic lithosphere with crustal structure and surface tectonics indicates a significant correlation between the deep, shallow, and near-surface structure of the lithosphere. The latter observation is illustrated by examples from the East European and the Siberian cratons, where Proterozoic sutures and intracratonic basins are manifested by an increase in mantle density as compared to light and strongly depleted lithospheric mantle of the Archean nuclei.