We design novel sun barriers of energy efficient buildings. Making use of morphing lattices, we design sun screens that can be opened and closed during different hours of the day and periods of the year, by controlling the stretching of a limited number of cables. The struts of the screens re-main undeformed during the opening and closure operations and can therefore support rigid plates, such as, e.g., solar panels and/or shading panels. Such morphing abilities lead us to the design of lightweight sun screens whose actuation requires reduced low energy consumption and minimal friction effects. We end with a review of novel "responsive architectures" for energy ef-ficient buildings, which make use of tensegrity structures at different levels (primary and second-ary structures) in order to respond to the natural environment by changing their mechanical and heating, ventilating and air-conditioning properties.