Petrological constitution of the upper mantle beneath the ocean floor has been poorly known except for oceanic fracture zones of slow-spreading ridges. Information from ophiolites may supplement the paucity of data to some extent; however, the ophiolites should be treated carefully because of their polygenetic nature. The abyssal peridotite varies from lherzolite with Cr# of spinel of 0.1 to harzburgite with Cr# of spinel of 0.6. Dunite is relatively rare from the ocean floor. An exotic lherzolite with continental with continental mantle signatures appears in mid-oceanic areas. The refractoriness of the abyssal peridotite has been proposed to correlate with the spreading rate of the ridge system, but this is false. The upper mantle beneath the ocean floor changes downwards from dunite to lherzolite via harzburgite, being independent of spreading rate. The lithological change is more abrupt in a slow-spreading system than in a fast-spreading one, so it is around ridge segment boundaries rather than around the segment center on the same spreading ridge. The thin harzburgite layer in slow-spreading ridges has resulted in its rarity there, and the deep seat of lherzolite in fast-spreading ridges has caused its apparent absence. The primitive MORB can be in equilibrium with dunite, which is formed along the melt conduit beneath the ridge via peridotite/melt reaction, and the dunite part is laid down by the corner flow of the mantle just below the lowermost gabbro layer as it leaves the ridge axis. We proposed the following deep ocean-floor drilling to explore scientific problems concerning the abyssal upper mantle: (1) non-riser drilling on the "continental peridotite" to know the relationship with abyssal peridotite, and (2) non-riser or riser drilling on the ocean floor where deep-seated rocks have already been exposed to examine the deep constitution of the upper mantle. The "21st Century Mohole" drilling through the oceanic Moho should primarily be directed to the segment center of a fast-spreading ridge system. The back-arc basin such as the Sea of Japan will be the alternate for Mohole drilling because we have had relatively little information on the petrological nature of the back-arc basin lithosphere despite its importance. We can solve the "ophiolite problem" simultaneously if we are careful in choosing the drilling sites. We also propose a close linkage between the ophiolite study and ocean drilling in the coming IODP.