We are going to show how using group schemes and functional identities allows one to
extend early results describing group gradings on classical simple Lie algebras over
fields of characteristic zero. Now we can work with simple Lie algebras of infinite
dimension (finitary simple Lie algebras), or simple modular Lie algebras, even not
necessarily classical, such as simple Cartan Lie algebras. More information is now
available about gradings on exceptional Lie algebras.