Epitaxy refers to the deposition of a crystalline overlayer on a crystalline substrate, where the overlayer is in registry with the substrate. In other words, there must be one or more preferred orientations of the overlayer with respect to the substrate for this to be termed epitaxial growth. The overlayer is called an epitaxial film or epitaxial layer. The term epitaxy comes from the Greek roots epi, meaning "above", and taxis, meaning "in ordered manner". It can be translated "to arrange upon". For most technological applications, it is desired that the deposited material form a crystalline overlayer that has one well-defined orientation with respect to the substrate crystal structure (single-domain epitaxy).

Epitaxial films may be grown from gaseous or liquid precursors. Because the substrate acts as a seed crystal, the deposited film may lock into one or more crystallographic orientations with respect to the substrate crystal. If the overlayer either forms a random orientation with respect to the substrate or does not form an ordered overlayer, this is termed non-epitaxial growth. If an epitaxial film is deposited on a substrate of the same composition, the process is called homoepitaxy; otherwise it is called heteroepitaxy.