The (BEDT)(2)X family of layered superconductors is one of the largest amon
g nearly 50 organic superconductors currently known. One of the advantages
of the organic compounds as prototype materials for studying the mechanisms
of superconductivity is their relatively high sensitivity to hydrostatic p
ressure. We review recent NMR studies of these compounds using NMR under li
quid and gas pressure. We focus on the low temperature part of the phase di
agram where the physics is controlled by electronic correlations leading to
a competition between magnetism and superconductivity. This interplay betw
een different ground states is shown by the observation of a pseudo-gap and
antiferromagnetic fluctuations and can be finely tuned by the application
of pressure. Using a gas pressure system gives the unique possibility of sw
eeping the pressure at low temperature. Recently we used this technique to
study the AF-SC boundary and established the existence of a first order tra
nsition line between the superconducting and antiferromagnetic states.