In this Special Issue, we have 10 excellent papers on epitaxy. In this editorial preface, I will make comments on the following issues: (1) applications of the materials examined, (2) lattice mismatch, (3) epitaxial growth methods used, (4) characterization methods used, (5) material problems: solved and still to be solved. The “Advances in Epitaxial Materials” has a big advantage of having, in one issue, papers on different materials, but in every paper the reader should find interesting information on epitaxial growth and characterization.