NMR spectroscopy is an indispensable method of analysis in chemistry, which until recently suffered from high demands for space, high costs for acquisition and maintenance, and operational complexity. This has changed with the introduction of compact NMR spectrometers suitable for small-molecule analysis on the chemical workbench. These spectrometers contain permanent magnets giving rise to proton NMR frequencies between 40 and 80 MHz. The enabling technology is to make small permanent magnets with homogeneous fields. Tabletop instruments with inhomogeneous fields have been in use for over 40 years for characterizing food and hydrogen-containing materials by relaxation and diffusion measurements. Related NMR instruments measure these parameters in the stray field outside the magnet. They are used to inspect the borehole walls of oil wells and to test objects nondestructively. The state-of-the-art of NMR spectroscopy, imaging and relaxometry with compact instruments is reviewed.