Layered intercalation compounds, which have a structure in which atoms or molecules (intercalants) are inserted into layered compounds (hosts), have been extensively studied because of their characteristic physical properties and the wide variety of synthetic methods available. Due to their ability to intercalate/de-intercalate ions and molecules, they are being investigated for applications in energy storage, and various properties resulting from their two-dimensional nature, such as superconductivity, spin glass, topological electronic states, have also been studied. Other novel phenomena have also been reported, such as the change in host electrowetting response and manipulation of magnetism due to molecule intercalation. As for synthesis methods, in addition to the general solid-phase, vapor-phase, ion-exchange, and electrochemical insertion methods, a wide variety of synthetic techniques such as zerovalent metal intercalation, liquid alloy, molten salt, molecular beam epitaxy, and chemical vapor deposition methods have been studied in recent years, and various new materials have been synthesized. However, there is no systematic understanding of which combinations of hosts and intercalants are stable, and thus, it is not straightforward to search for new layered intercalation compounds from a vast number of combinations.