  This chapter provides a review of microscopic theories of pairing in nuclear
systems and neutron stars. Special attention is given to the mean-field BCS
theory and its extensions to include effects of polarization of the medium and
retardation of the interactions. Superfluidity in nuclear systems that exhibit
isospin asymmetry is studied. We further address the crossover from the
weak-coupling BCS description to the strong-coupling BEC limit in dilute
nuclear systems. Finally, within the observational context of rotational
anomalies of pulsars, we discuss models of the vortex state in superfluid
neutron stars and of the mutual friction between superfluid and normal
components, along with the possibility of type-I superconductivity of the
proton subsystem.
