This paper has made an overview on elastic and structural aspects of three distinct superlattices under hydrostatic pressure up to about 8GPa, which were studied by our unique x-ray diffraction technique incorporated with a diamond-anvil cell. They are metallic fcc/fcc Au/Ni, bcc/fcc Mo/Ni, and semiconductive epitaxially-grown PbSe/SnSe superlattices. In their layer-stacking direction, both metallic superlattices show the supermodulus behavior while the semiconductive one doesn't. However, its pressure-driven cubic-to-orthorhombic phase transition, successively taking place in the SnSe and PbSe layers, has been found to significantly shift by stress due to its epitaxial growth.