The methodology of NMR experiments intended to measure anisotropic diffusion is reviewed. Experiments of this kind preferably require oriented samples and/or orientation-dependent spin coupling and/or magnetic field gradients in different directions. One strategy of diffusion experiments in anisotropic systems with broad NMR lines employs line narrowing techniques, thereby allowing for efficient gradient encoding/decoding. Depending on the nuclei, spin couplings and samples, the preferred methods vary from decoupling through echo techniques to magic angle sample orientation and spinning. Another avenue to efficient gradient encoding/decoding is through very strong magnetic field gradients. Either way, anisotropic diffusion reveals new structural features as illustrated by a few selected examples in liquid crystals and in biological tissues.