This review presents the status of the field of two-nucleon and multi-nucleon transfer reactions induced by heavy ions. The role of the pairing interaction in nuclei as a finite quantum system is illustrated. These reactions serve as a unique tool for the study of the dynamical aspects of pairing correlations in nuclei in particular for the cases of nuclear superfluidity. The new possibilities offered by the development of experimental techniques, e.g. the large gammaray detectors combined with charged particle detectors are presented, which allows the study of the enhanced pair transfer between well selected states, and the problem of the expected quenching of pairing correlation at high spin. Further, the new possibilities offered by the advent of radioactive beam facilities are discussed.