We review recent NMR studies of a layered organic superconductor of th
e (BEDT)(2)X family. First the normal state properties are discussed.
The central issue is the importance of the interplay between antiferro
magnetism and superconductivity in these materials demonstrated by the
observation of a pseudogap developing prior to the superconducting tr
ansition. The use of high pressure to tune the amplitude of AF fluctua
tions enables us to draw a general phase diagram of the family. In the
second part the NMR experiments in the superconducting state are pres
ented. One of the fundamental questions addressed by these experiments
is the symmetry of the order parameter related to the pairing mechani
sm. The most spectacular NMR measurements are those performed in the l
ock-in state, which give access to the density of superconducting exci
tations at low energy. These experiments suggest that the pairing stat
e may be unconventional featuring an anisotropic superconducting gap,
possibly with nodes.