The magnetic field gradient nuclear magnetic resonance (NMR) stimulated echo experiment measures the incoherent (or self) part of the intermediate scattering function S( Q,t) ∼ 〈 exp[ − i Qr(O)] exp[ i Qr(t)]〉 with a ‘generalized’ scattering vector Q = γ· g·τ (γ is the gyromagnetic ratio, g is the magnetic field gradient, τ is the evolution time). With ultrahigh static field gradients up to ≈ 180 T/m, a prototype of which has recently been installed in Mainz, Q-values up to > 10 −2 Å −1 become accessible. The first part of the paper focusses on details of this technical development and points out the close analogy with incoherent neutron scattering. In the second part, the enormous new possibilities of this kind of gradient NMR are demonstrated through a collection of most recent applications: the measurement of small self-diffusion coefficients down to about 10 −15 m 2s −1 in supercooled liquids and in molecular crystals, long chain polymer dynamics, restricted diffusion in systems of confined mesocopic geometries and anomalous diffusion on fractal structures.