After recalling the main results in the theory of Galois module structures of rings of integers of finite extensions of Q, we will consider relative situations when the base field is an arbitrary number field. We will show how the classical question of the existence of normal integral basis generalizes when dealing with torsors associated with the points of the Mordell-Weil group of an elliptic curve. Finally we will indicate how these arithmetic questions lead to problems on torsion line bundles on abelian schemes.