An exemplary morphable ceramic composite structure includes a flexible ceramic composite skin and a truss structure attached to the skin. The truss structure can morph shape of the skin from a first shape to a second shape that is different than the first shape. The flexible ceramic composite skin may include a single-layer of three-dimensional woven fabric fibers and a ceramic matrix composite. The truss structure may include at least one actuatable element or an actuator may move a portion of the truss structure from a first position to a second position. A cooling component may be disposed in thermal communication with the skin. The cooling component may include thermal insulation or a cooling system that circulates cooling fluid in thermal communication with the skin. The morphable ceramic composite structure may be incorporated into any of an air inlet, combustor, exhaust nozzle, or control surfaces of a hypersonic aircraft.