Ionic liquids, and their solid-state equivalents organic ionic plastic crystals, show many useful and tailorable properties that make them interesting for a wide range of applications including as electrolytes for energy storage devices. Nuclear magnetic resonance spectroscopy and related techniques offer a powerful and versatile toolkit for the characterisation of structure, interactions and dynamics in these materials. This article summarises both commonly used methods and some recent advances in this area, including solution- and solid-state methods, dynamic nuclear polarisation, imaging, diffusion and relaxation measurements, and example applications of some less commonly studied nuclei.