One of the major obstacles to realizing various kinds of epitaxial heterostructure is the lattice matching between constituent materials. The lattice-matching condition, however, has been found to be drastically relaxed when the epitaxial growth proceeds with van der Waals interactions. Many kinds of layered material are suitable for that purpose. They are easily cleaved along the layers without producing dangling bonds on their cleaved surfaces. The epitaxial growth of a layered material onto those surfaces proceeds with a van der Waals force, resulting in good heteroepitaxial growth even with a large lattice mismatch between the grown and the substrate materials. It has also been found that van der Waals epitaxy can be applied to the epitaxial growth of a layered material on an ordinary three-dimensional material substrate, if regular termination of the surface dangling bonds is accomplished. Sulphur or selenium-atom-terminated GaAs(111), H-atom-terminated Si(111) and F-atom-terminated CaF2(111) surfaces can be used for that purpose. van der Waals epitaxy has also been successfully applied to grow such organic molecular crystal films as metal phthalocyanines, higher aromatics and C60.