Membrane Optical Shell Technology (MOST) is an innovative combination of 1) very low areal density (40 to 200g/m2) optically smooth (<20 nm rms), metallic coated reflective membrane thin films, 2) advanced fabrication techniques that transform the films into self supporting shells through the introduction of permanent optically relevant double curvature, and 3) discrete active boundary control to enable rigid body alignment and maintainment of surface figure in face of environmental disturbances. Areal densities of better than 2 kg/m2 (including actuators) are projected. Current measured surface figure is ≈1 to 10 microns rms at up to the 15 cm size, and we are poised for further improvements. Demonstrated material and fabrication techniques are scaleable to at least the 2m+ diameter single surface apertures and larger apertures are possible through segmentation techniques. Proven stowage and deployment techniques enable space flight application. We propose advancing 1) the basic fabrication technology and 2) the TRL level of MOST apertures for ground and space based apertures. The key resulting innovation is implementation of low areal density, compact roll stowable approaches to realize low mass, low cost reflective apertures for RF/Microwave to LIDAR. Other NASA and DOD applications are expected as precision and aperture size increase.