The advantages of pulsed laser deposition for oxide film growth and of molecular beam epitaxy for two-dimensional film growth were combined to develop a method for atomically controlled layer-by-layer epitaxy of complex oxides and other ceramic thin films. This laser MBE method has been proved to be particularly useful for the purpose. Two-dimensional molecular layer epitaxy has been verified by the clear observation of RHEED intensity oscillations for the growth of various ceramics including perovskites, infinite-layer cuprates, rock salt oxides, corundum, and fluorites on oxide substrates. Epitaxial growth of BaTiO3, BaO and sapphire films was achieved even at such a low temperature as 20 degrees C. Some phenomena indicating novel quantum effects were observed in high quality ZnO film and SrTiO3/SrVO3 superlattice, both fabricated by laser MBE. In view of the versatility and structure-sensitive properties of oxides, lattice engineering by laser MBE is expected to be a promising technology for opening a new field of oxide electronics.