[en] Multilayer-coated Blazed Gratings (MBG) can offer high diffraction efficiency in a very high diffraction order and are therefore of great interest for high-resolution EUV and soft x-ray spectroscopy techniques such as Resonance Inelastic X-ray Scattering. However, realization of the MBG concept requires nano-scale precision in fabrication of a saw-tooth substrate with atomically smooth facets, and reproduction of the blazed groove profile in the course of conformal growth of a multilayer coating. We report on recent progress achieved in the development, fabrication, and characterization of ultra-dense MBGs for EUV and soft x-rays. As a result of thorough optimization of all steps of the fabrication process, an absolute diffraction efficiency as high as 44% and 12.7% was achieved for a 5250 l/mm grating in the EUV and soft x-ray regions respectively. This work now shows a direct route to achieving high diffraction efficiency in high order at wavelengths throughout the soft x-ray energy range with revolutionary applications in synchrotron science.