At geological time-scales, the mantle behaves as a high Rayleigh number fluid, i.e., thermal convection takes place and produces cells circulating at variable sizes and speeds. A lot of effort has been made to understand the upwelling part of these cells occurring underneath ridges and hotspots where they give birth to volcanoes. Nevertheless, local passive (adiabatic) sub-lithospheric mantle upwellings are likely to be more widespread and even common below oceanic plates. Just like under volcanoes, mantle is expected to undergo decompression melting in these concealed upwelling regions but the magma produced may be trapped and not have any volcanic expression. Here, we intend to discuss the fate of these deep melts and try to present a broad view of their geophysical and geochemical expressions. In our analyses, we model mantle melting that is favored by two critical parameters: high temperatures and/or elevated concentrations of H2O and CO2. It is frequently modeled as a chemical process in a static system, where thermodynamics is used to define the quantity of melts produced as a function of temperature and volatile contents. On the other hand, fluid mechanics tell us that the melt produced having low viscosity and low density tends to migrate away from its solid source at a rate depending on a variety of physical parameters; permeability and density/viscosity contrasts being the most influent. Combining thermodynamics and fluid mechanics, we show that CO2-H2O melts tend to focus at the lithosphere-asthenosphere boundary, where melt contents can reach 1-2%. This can easily explain many geophysical observations on the LVZ. The magnitude of the geophysical signal at the LVZ is related to convection (upwelling) in the asthenosphere; upwelling produces decompression-melting and the melt tends to accumulate below the impermeable lithosphere. The lithosphere-asthenosphere boundary must be featured by a strong and focused weakening where strain localizations enable decoupling between the plates and the asthenosphere. This geodynamic configurations is probably not always conceivable, particularly during the Archean, since temperatures was much hotter and melting much deeper.