  In spite of the absence of viscous drag, the neutron superfluid permeating
the inner crust of a neutron star cannot flow freely, and is entrained by the
nuclear lattice similarly to laboratory superfluid atomic gases in optical
lattices. The role of entrainment on the neutron superfluid dynamics is
reviewed. For this purpose, a minimal hydrodynamical model of superfluidity in
neutron-star crusts is presented. This model relies on a fully
four-dimensionally covariant action principle. The equivalence of this
formulation with the more traditional approach is demonstrated. In addition,
the different treatments of entrainment in terms of dynamical effective masses
or superfluid density are clarified. The nuclear energy density functional
theory employed for the calculations of all the necessary microscopic inputs is
also reviewed, focusing on superfluid properties. In particular, the
microscopic origin of entrainment and the different methods to estimate its
importance are discussed.
