An underwater drilling rig in modular form, which can be simply assembled underwater and in which standard tubulars and tubular assemblies are stored in a novel arrangement within containers and can be added to, and removed from, the string in the well bore, whilst there is continuous circulation of drilling fluid and also continuous segregation of drilling fluid from the seawater; additionally: with a simple means of accessing the tubulars and gripping them from inside in order to make up tool joint connection to the top drive sub, with a means to guide and centralise each tubular or tubular assembly on entering the well bore or when being returned to storage, with a means to enable the top drive to snub with greatly reduced force and no risk of buckling the tubular; with a rig support vessel that, in the absence of a marine riser, drill string or drilling rig, is greatly reduced in size and can roam extensively to ride out bad weather, while the seabed rig continues to drill; lastly with the novel ability to control the mud pressure and flow both in and out of the well bore at seabed level, thus greatly improving downhole pressure strategy; ultimately the first system that can operate at water depths of 10,000 to 20,000 feet which is still beyond the current economic and technical ability of offshore drilling rigs.