  Cosmological analysis based on currently available observations are unable to
rule out a sizeable coupling among the dark energy and dark matter fluids. We
explore a variety of coupled dark matter-dark energy models, which satisfy
cosmic microwave background constraints, in light of low redshift and near
universe observations. We illustrate the phenomenology of different classes of
dark coupling models, paying particular attention in distinguishing between
effects that appear only on the expansion history and those that appear in the
growth of structure. We find that while a broad class of dark coupling models
are effectively models where general relativity (GR) is modified --and thus can
be probed by a combination of tests for the expansion history and the growth of
structure--, there is a class of dark coupling models where gravity is still
GR, but the growth of perturbations is, in principle modified. While this
effect is small in the specific models we have considered, one should bear in
mind that an inconsistency between reconstructed expansion history and growth
may not uniquely indicate deviations from GR. Our low redshift constraints
arise from cosmic velocities, redshift space distortions and dark matter
abundance in galaxy voids. We find that current data constrain the
dimensionless coupling to be |xi|<0.2, but prospects from forthcoming data are
for a significant improvement. Future, precise measurements of the Hubble
constant, combined with high-precision constraints on the growth of structure,
could provide the key to rule out dark coupling models which survive other
tests. We shall exploit as well weak equivalence principle violation arguments,
which have the potential to highly disfavour a broad family of coupled models.
