The footprints of mafic melts travelling from the depths to the surface are abundant in the mantle section of ophiolites. They constitute an important source of information about the melt migration mechanisms and related petrological processes in the shallowest part of the mantle beneath former oceanic spreading centres. In the field, these so-called ‘melt migration structures’ attract attention when they consist of mineral assemblages contrasting with that of their host peridotite. They therefore record a particular moment in the migration history: when the melt becomes out of equilibrium with the peridotite and causes a reaction impacting its modal composition, and/or when a temperature drop initiates the crystallization of the melt. The existence of cryptic effects of migration revealed by geochemical data shows that melts do not always leave a trail visible in the field. Although incomplete and patchy, the melt migration structures preserved in ophiolites are witnesses of processes that do actually occur in nature, which constitutes an invaluable support to the interpretation of geophysical data and inescapable constraints for numerical simulations and models of chemical geodynamics. Here we show how field observations and related petrological and geochemical studies allow us to propose answers to fundamental questions such as these: At which temperature is porous flow superseded by dyking? What are the factors governing melt trajectories? What is the nature of the ‘universal solvent’ initiating infiltration melting and making channelized porous flow the most common mode of transport of magmas through a peridotite matrix regardless the tectonic setting? A fundamental message delivered by ophiolites is that the shallow mantle behaves as a particularly efficient reactive filter between the depths and the surface of the Earth. Unexpectedly, the reactions occurring there are enhanced by the hybridization between mafic melts and a hydrous component, whatever its origin ( i.e. magmatic vs. hydrothermal). This hybridization triggers out of equilibrium reactions, leading to the formation of exotic lithologies, including metallic ores, and impacting the global geochemical cycle of a whole range of chemical elements.