  Pairing effects manifests themselves in many aspects in nuclear systems
ranging from finite nuclei to nuclear matter and compact stars. Although with
some specific features for nuclear systems, the mechanism of pairing between
nucleons in these systems resembles that of electrons in superconductors. The
Bardeen-Cooper-Schrieffer (BCS) theory, the first successful and microscopic
theory for superconductivity, and the Bogoliubov transformation, the
generalization of the BCS theory, have been widely used to describe pairing
correlations in nuclear systems. To deal with the problem of particle number
non-conservation in the BCS method and generalized Bogoliubov transformation,
particle number projection techniques as well as several approaches which keep
the particle number conserved, have been proposed. In the study of exotic
nuclei, which are quantum open systems, the continuum contributions have to be
taken into account. In this chapter, a thorough but brief discussion of pairing
effects in nuclear systems will be introduced. Then nuclear models dealing with
pairing correlations in nuclear structure properties will be presented to
different extent of details. Although formulas are given, the emphasis is
mainly put on the basic ideas concerning these models.
