The role of neutron–proton pairing correlations on the structure of nuclei along the N=Z line is reviewed. Particular emphasis is placed on the competition between isovector (T=1) and isoscalar (T=0) pair fields. The expected properties of these systems, in terms of pairing collective motion, are assessed by different theoretical frameworks including schematic models, realistic Shell Model and mean field approaches. The results are contrasted with experimental data with the goal of establishing clear signals for the existence of neutron–proton (np) condensates. We will show that there is clear evidence for an isovector np condensate as expected from isospin invariance. However, and contrary to early expectations, a condensate of deuteron-like pairs appears quite elusive and pairing collectivity in the T=0 channel may only show in the form of a phonon. Arguments are presented for the use of direct reactions, adding or removing an np pair, as the most promising tool to provide a definite answer to this intriguing question.