This will be a colloquium-style talk giving a survey of certain classical results concerning the Galois structure of rings of integers. Starting with an elementary result in Galois theory (the normal basis theorem), one is led to a remarkable connection between the Galois module structure of rings on integers on the one hand, and the behaviour of certain analytical objects called Artin L-functions. I shall discuss this connection and how it fits into a much broader picture than one might have at first suspected.