It is now just over 50 years since Erwin Hahn's first paper on the phenomenon of the spin echo, in which he noted that the formation of echoes could be disrupted by diffusion. This proved to be a significant observation, paving the way for a whole range of experimental methods to investigate both coherent and incoherent molecular motion. NMR can now measure the velocities of motions slower than continental drift, and detect average molecular displacements of the order of nanometres. One spectacular, and surely unanticipated, application of Hahn's observation has been the development of techniques for mapping the motion of blood and other fluids in the human body.
While the study of diffusion by NMR has made many important contributions over the years, until recently it was the province largely of those specialists with the skills needed to construct and maintain the special apparatus required. The recognition that pulsed field gradients can greatly improve the speed and spectral quality of multidimensional NMR, coupled with developments such as actively shielded gradient coils, has now led to pulsed field gradient capabilities becoming almost universal on modern routine high resolution spectrometers. As a result, diffusion measurements on all but the largest species are now within the scope of most NMR laboratories, and there has been a blossoming both of chemical applications of NMR diffusion measurements, and of new techniques for making such measurements. This special issue of the journal Magnetic Resonance in Chemistry illustrates both the very wide range of systems that can now profitably be studied, from gases through natural products and biomolecules to synthetic polymers and colloids, and the great variety of instrumental and data processing techniques which can contribute to our understanding and exploitation of the phenomenon of diffusion.