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We review several experimental and theoretical advances that emphasise commonaspects of the study of T=1 and T=0 pairing correlations in nuclei. We firstdiscuss several empirical evidences of the special role played by the T=1pairing interaction. In particular, we show the peculiar features of thenuclear pairing interaction in the low density regime, and possible outcomessuch as the BCS-BEC crossover in nuclear matter and, in an analogous way, inloosely bound nuclei. We then move to the competition between T=1 and T=0pairing correlations. The effect of such competition on the low-lying spectrais studied in N=Z odd-odd nuclei by using a three-body model; it is shown thatthe inversion of the 0+ and 1+ states near the ground state, and the strongmagnetic dipole transitions between them, can be considered as a clearmanifestation of strong T=0 pairing correlations in these nuclei. The effect ofT=0 pairing correlations is also quite evident if one studies charge-changingtransitions. The Gamow-Teller (GT) states in N=Z+2 nuclei are studied here byusing self-consistent HFB+QRPA calculations in which the T=0 pairinginteraction is taken into account. Strong GT states are found, near the groundstate of daughter nuclei; these are compared with available experimental datafrom charge-exchange reactions, and such comparison can pinpoint the value ofthe strength of the T=0 interaction. Pair transfer reactions are eventuallydiscussed: while two-neutron transfer has been long proposed as a tool tomeasure the T=1 superfluidity in the nuclear ground states, the study ofdeuteron transfer is still in its infancy, despite its potential interest inrevealing effects coming from both T=1 and T=0 interactions.

Isovector spin-singlet (T=1, S=0) and isoscalar spin-triplet (T=0, S=1) pairing interactions and spin-isospin response