This thesis studies the dynamics of mantle melting during continental breakups by geophysical, geochemical, and numerical analyses. The first part focuses on the mantle melting and crustal accretion processes during the formation of the Southeast Greenland margin, on the basis of deep-crustal seismic data. A seismic tomographic method is developed to jointly invert refraction and reflection travel times for a compressional velocity structure. Together with gravity data, the velocity structure is used to resolve the origin of a margin gravity high. A robust framework is developed for the petrological interpretation of crustal velocity structure, and vigorous active upwelling of normal mantle is suggested to be responsible for the extensive rifting magmatism. In the second part, the nature of mantle melting during the formation of the North Atlantic igneous province is studied based on the major element chemistry of erupted lavas. The results suggest that this province is characterized by strong major element source heterogeneity. In the third part, the nature of preexisting sublithospheric convection is investigated by a series of finite-element analyses, and the results suggest that small-scale convection is likely in normal asthenosphere, and that the upwelling velocity in such convection is on the order of 1-10 cm per year.