  We discuss several pairing-related phenomena in nuclear systems, ranging from
superfluidity in neutron stars to the gradual breaking of pairs in finite
nuclei. We describe recent experimental evidence that points to a relation
between pairing and phase transitions (or transformations) in finite nuclear
systems. A simple pairing interaction model is used in order to study and
classify an eventual pairing phase transition in finite fermionic systems such
as nuclei. We show that systems with as few as 10-16 fermions can exhibit clear
features reminiscent of a phase transition.
