Melting and melt segregation are key processes in the geochemical evolution of the Earth. However, mechanism and time scale of melt transport from the source to the surface are still not well understood and are dependent on the grain-scale distribution of melt. A related question is the retention of melt in partially molten regions of the Earths upper mantle. Seismic observations from mid-ocean ridges (MOR) and subduction zones are interpreted to show in-situ melt contents up to 3%, while geochemical observations from MOR basalts are inferred to indicate very efficient extraction of melt (porosities of order 0.1%). Earlier theoretical models of the melt distribution were based on the balance of surface tension between melt and uniform crystalline grains, predicting a simple net- work of melt along three-grain edges. Analyses of experimentally produced samples of olivine and basaltic melt show that the melt geometry is much more complex, and includes wetted two-grain boundaries. I reconstructed the melt geometry of two experimentally produced samples by serial sectioning and 3-D rendering of the pore geometry which demonstrates for the first time that melt exists in thin layers on two-grain boundaries. This confirms the inferences from previous 2-D observations and has significant implications for physical properties of partially molten regions, for example seismic velocities and attenuation. The wetted two-grain boundaries are inferred to be a consequence of continuous grain growth. Due to the complexity of the 3-D melt geometry the perme- ability of partially molten rocks can not be predicted from simple models. I therefore investigated the permeability as a function of porosity for both synthetic and ex- perimentally determined pore geometries using a lattice-Boltzmann method. The calculated permeability is not a simple function of porosity, but increases rapidly at a critical fraction of wetted two-grain boundaries. In order to extrapolate the experimentally based findings to grain sizes expected in natural rocks I examined the geometry of secondary phases inferred to represent relict melt in mantle peridotites from the Krivaja massif in Bosnia. These findings corroborate the experimental observations of wetted two-grain boundaries.