  We discuss the response of neutron stars to the tidal interaction in a
compact binary system, as encoded in the Love number associated with the
induced deformation. This problem is of interest for gravitational-wave
astronomy as there may be a detectable imprint on the signal from the late
stages of binary coalescence. Previous work has focussed on simple barotropic
neutron star models, providing an understanding of the role of the stellar
compactness and overall density profile. We add realism to the discussion by
developing the framework required to model stars with varying composition and
an elastic crust. These effects are not expected to be significant for the next
generation of detectors but it is nevertheless useful to be able to quantify
them. Our results show that (perhaps surprisingly) internal stratification has
no impact whatsoever on the Love number. We also show that crust elasticity
provides a (predictably) small correction to existing models.
