Atomic and molecular beams have been used extensively to probe fundamental physical and chemical properties of atoms and molecules. A new application of molecular beams for materials synthesis is emerging. The unique properties of supersonic molecular beams which make this new application to thin film growth promising are described. Problems encountered in the implementation of supersonic jet epitaxy (SJE) as well as growth conditions favorable for the incorporation of real-time, in situ monitoring are discussed. The advantages and disadvantages of different precursors for the growth of cubic-SiC on Si are compared. The growth rate and morphology of the grown films are shown to depend on the kinetic energy of the precursors and the growth temperature. Enhancing the kinetic energy of precursors also led to lower growth temperatures for single crystal GaN and AlN thin films on silicon based substrates. Problems which remain to be solved in SJE of wide band gap semiconductors are summarized.