Diffusion in solids, which requires the presence of crystal defects or disorder, has both microscopic and macroscopic aspects. Nuclear magnetic resonance techniques provide access to microscopic diffusion parameters like atomic jump rates and activation energies as well as to the tracer diffusion coefficient for macroscopic transport. Microscopic NMR methods include spin-lattice relaxation spectroscopy of stable and beta-radioactive nuclei, spin-spin relaxation or linewidth and spin alignment decay measurements, whereas macroscopic NMR methods are represented by the techniques of static and pulsed field gradient NMR. We recall some basic principles of the mentioned techniques and review case studies for their application to various solids like glassy and crystalline aluminosilicates, nanocrystalline composites, an intercalation compound and a simple bcc metal. Taken together, jump rates in solids are covered over about 10 decades by the microscopic, and diffusion coefficients over 3 decades by the macroscopic NMR methods.