First principles electronic structure calculations and high resolution transmission electron microscopy were used to study the interface of diamond with beryllium oxide (BeO) and cubic boron nitride (c-BN). These are the tetrahedrally coordinated, covalently bonded solids that are most closely lattice-matched to diamond. The theoretical results indicate that diamond should adhere strongly to both BeO and c-BN. Diamond deposited on the Be terminated (0001) surfaces of BeO by hot-filament assisted deposition showed local epitaxy of isolated diamond crystals. Parallel epitaxy of diamond films was achieved on the B terminated (111) surfaces of c-BN. Diamond, Beryllium oxide, Cubic boron nitride, Heteroepitaxy, Chemical vapor deposition.