A fast field cycling NMR (FFC NMR) experiment measures the longitudinal (spin-lattice) relaxation rate as a function of applied magnetic field to yield a relaxation rate dispersion curve,  where  is the proton Larmor frequency.  The  dispersions, or NMRD profiles, are exquisitely sensitive to the relative dynamics of proton spins across timescales in the range 10^-9-10^-4 s. These timescales span the translational and rotational dynamics of proton-bearing fluids to dynamics at the surfaces of solids, soft material and macromolecules. FFC NMR is useful for studying fluid-filled rocks and soils, porous silica and cementitious material, polymer systems, foodstuffs, protein systems, biological tissues and biofluids. The NMRD profiles are rich with information, but interpretation is challenging. A parametrized relaxometry model must generate an NMRD profile  that can be fit to experimental data across 3-4 orders of magnitude of frequency. The 3-Tau Model has emerged as a model capable of fitting NMRD profiles from a broad range of material types yielding physically meaningful parameters. This review article demonstrates power of the FFC NMR experiment interpreted using the 3-Tau Model to reveal properties of hydrated hard and soft material.