This talk will give an introduction to vertex operator algebras over an arbitrary field. In particular, the rationality of the vertex operator algebra associated to the highest weight modules for the Virasoro algebra with central charge 1/2 is established and the irreducible modules are classified. Moreover, we investigate modular framed vertex operator algebras. In particular, the rationality of modular framed vertex operator algebras is established. For a modular code vertex operator algebra, the irreducible modules are constructed and classified.