Epitaxial alignment has been obtained by means of grain growth in polycrystalline films deposited on single‐crystal substrates. A theory for epitaxial grain growth is outlined and results given for experiments on Au, Al, Cu, and Ag films on vacuum‐cleaved NaCl, KBr, KCl, or mica. Epitaxial grain growth provides a fundamentally different alternative to conventional epitaxy, and can lead to very thin films with improved continuity and crystalline perfection, as well as non‐lattice‐matched orientations.