Abstract : This treatise is a collection of introductory chapters and published articles on pairing and superfluidity in various fermionic many-body systems: trapped atomic gases, nuclear matter, neutron star crust, droplets of quark matter ("strangelets"). After a general introduction, emphasizing the analogies between these different systems, pairing in static systems is discussed: Bogoliubov-de Gennes (Hartree-Fock-Bogoliubov) equations for finite systems, Nozières-Schmitt-Rink approach for the BEC-BCS cross-over. Then the collective motion of superfluid systems is studied: slow rotation (without vortex) and collective modes. This is done in the framework of the following methods: superfluid hydrodynamics, quasiparticle random-phase approximation (QRPA), and semiclassical theories (quasiparticle transport theory by Betbeder-Matibet and Nozières, Boltzmann equation). Finally, perspectives and future projects are discussed.