  The Giant Pairing Vibration, a two-nucleon collective mode originating from
the second shell above the Fermi surface, has long been predicted and expected
to be strongly populated in two-nucleon transfer reactions with cross sections
similar to those of the normal Pairing Vibration. Recent experiments have
provided evidence for this mode in $^{14,15}$C but, despite sensitive studies,
it has not been definitively identified either in Sn or Pb nuclei where pairing
correlations are known to play a crucial role near their ground states. In this
paper we review the basic theoretical concepts of this "elusive" state and the
status of experimental searches in heavy nuclei. We discuss the hindrance
effects due to Q-value mismatch and the use of weakly-bound projectiles as a
way to overcome the limitations of the (p,t) and (t,p) reactions. We also
discuss the role of the continuum and conclude with some possible future
developments.
