Any oriented 4-dimensional real vector bundle is naturally a line bundle over
a bundle of quaternion algebras. In this paper we give an account of modules
over bundles of quaternion algebras, discussing Morita equivalence,
characteristic classes and K-theory. The results have been used to describe
obstructions for the existence of almost quaternionic structures on
8-dimensional Spinc manifolds and may be of some interest, also, in
quaternionic and algebraic geometry.