The growth of an epitaxial insulator on a semiconductor substrate and its subsequent overgrowth with an epitaxial semiconductor has a number of important applications, including the construction of three-dimensional devices, better isolation of devices in VLSI circuits, improved gate insulators, and optoelectronic devices. In addition, it presents a unique opportunity to study an insulator/semiconductor interface under controlled conditions. Many of the fluoride compounds are excellent insulators and can be grown epitaxially by MBE on many common semiconductors. Thus, epitaxial fluoride growth is being extensively studied at a number of laboratories. In our laboratory, the growth of epitaxial CaF2 on Si substrates and subsequent overgrowth with Si or Ge has been studied. While epitaxial growth of CaF2 (which has an fcc lattice structure as does Si) can be obtained on (100), (110), and (111) oriented Si substrates, the best quality crystal growth and surface morphology is obtained on (111) substrates, as the (111)CaF2 surface has the lowest free energy. Epitaxial Si overgrowth of the (111)CaF2 layers generally results in a high density of planar defects near the Si/CaF2 interface. However, epitaxial Ge overlayers have been grown with much lower defect densities.