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The Archimedean renewable energy systems are enjoying a renewed interest, since about one decade, and have become increasingly popular throughout Europe. It seems that this low head Archimedean technology is still a niche product. Despite the age of the Archimedean screws there is no consistent and appropriate theory for the screw hydraulic design linking the screw's geometry with their performances. This paper after giving a brief history of the Archimedean screw pumps and screw turbines presents an eagle's view of the recent NTUA and ASPETE Computational Fluid Dynamics (C.F.D.) modelling results, of the carried out within the program ARCHIMEDES III research, entitled "Rebirth of Archimedes: contribution to the study of hydraulic mechanics and hydrodynamic behavior of Archimedean cochlear waterwheels, for recovering the hydraulic potential of natural and technical watercourses, of maritime and tidal currents". [ABSTRACT FROM AUTHOR]