The main developments taking place in Nuclear Magnetic Resonance Spectroscopy (NMR) of quadrupolar (spin I > 1/2) nuclei with half integer spins in solids, particularly clays and other layered materials, have been reviewed. The advent of Multiple-Quantum (MQ) Magic-Angle Spinning (MAS) NMR spectroscopy has been a step-change development to the studies of quadrupolar nuclei in solids. It is now possible to record high-resolution spectra of important nuclei, such as 11B, 17O, 23Na, 27Al and 69,71Ga, in synthetic and natural clays. Since its introduction in 1995 MQMAS NMR has evolved considerably and, at present, a range of very useful related techniques are available and have been reviewed, as has the current situation with regard to applications to clays and other layered materials.