  The natural generalization of the notion of bundle in quantum geometry is
that of bimodule. If the base space has quantum group symmetries one is
particularly interested in bimodules covariant (equivariant) under these
symmetries. Most attention has so far been focused on the case with maximal
symmetry -- where the base space is a quantum group and the bimodules are
bicovariant. The structure of bicovariant bimodules is well understood through
their correspondence with crossed modules.
  We investigate the ``next best'' case -- where the base space is a quantum
homogeneous space and the bimodules are covariant. We present a structure
theorem that resembles the one for bicovariant bimodules. Thus, there is a
correspondence between covariant bimodules and a new kind of ``crossed''
modules which we define. The latter are attached to the pair of quantum groups
which defines the quantum homogeneous space.
  We apply our structure theorem to differential calculi on quantum homogeneous
spaces and discuss a related notion of induced differential calculus.
