The state of the art of the problem of mantle melt transport through the upper mantle beneath spreading zones is reviewed. The geochemical data and physical properties of the mantle constraining the melt migration processes are considered. The review concentrates on the ways of mantle magma transport and mechanisms of the localization of diffuse intergranular porous melt percolation into the channel flow. The hypothesis of the reaction of migrating mantle magmas with wall peridotites and the formation of replacive dunites as a result of this process are discussed. We examine the publications on the field, theoretical, and geochemical studies of the reactive melt migration and its role in the dunite formation in the mantle sections of the ophiolites. Alternative models of the dunite origin in the mantle are also tested. The results of experimental studies of the melt/peridotite interaction are presented.