Compounds with cage-like structures of elemental silicon and carbon are comparatively reviewed. Barium containing silicon clathrate compounds isomorphous with type I gas hydrates were prepared using high pressure and high temperature (HPHT) conditions, and found to become superconductors. The application of HPHT conditions to Zintl binary silicides have produced a number of silicon-rich cage-like structures including new clathrate structures; most of them are superconductors. Carbon analogs of silicon clathrates can be prepared by 3D polymerization of C60 under HPHT conditions, which are new allotropes of carbon with expanded framework structures. The crystal chemistry and characteristic properties of some related compounds are also reviewed.