Knowledge of distribution and transport mechanism of melt in the Earth and planetary interiors is important for understanding formation process of stratified structure, estimation of melt fraction in partial molten region, and volatile recycling. In this article, advances in high pressure studies on melt distribution and its transport process were reviewed in terms of surface tension-driven process. Melt migration in solid media is controlled by melt connectivity. A traditional way to determine melt connectivity is determination of dihedral angle by quench experiments. Recently, in situ X-ray radiographic observation or electrical conductivity measurement are developing as effective ways to determine melt morphology. At the end of this article, an example of melt penetration experiments is reported. High pressure experiments on penetration of metallic iron alloy melt into lower mantle phases suggest absence of interaction between core and mantle by surface-tension driven penetration mechanism.