Due to the single-particle character of the quadrupolar interaction in molecular systems, H-2 NMR poses a unique method for probing reorientational dynamics. Spin-lattice relaxation gives access to the spectral density, and its frequency dependency can be monitored by field cycling (FC) techniques. However, most FC NMR studies employ H-1; the use of H-2 is still rare. We report on the application of H-2 FC NMR for investigating the dynamics in molecular liquids and polymers. Commercial as well as home-built relaxometers are employed accessing a frequency range from 30 Hz to 6 MHz. Due to low gyromagnetic ratio, high coupling constants, and finite FC switching times, current H-2 FC NMR does not reach the dispersion region in liquids (toluene and glycerol), yet good agreement with the results from conventional high-field (HF) relaxation studies is demonstrated. The pronounced difference at low frequencies between H-2 and H-1 FC NMR data shows the relevance of intermolecular relaxation in the case of H-1 NMR In the case of the polymers polybutadiene and poly(ethylene-alt-propylene), very similar relaxation dispersion is observed and attributed to Rouse and entanglement dynamics. Combination with HF H-2 relaxation data via applying frequency temperature superposition allows the reconstruction of the full spectral density reflecting both polymer as well as glassy dynamics. Transformation into the time domain yields the reorientational correlation function C-2(t) extending over nine decades in time with a long-time power law, C-2(t) alpha t(-0.45 +/- 0.05), which does not conform to the prediction of the tube-reptation model, for which alpha t(-0.25) is expected. Entanglement sets in below C-2(t = tau(e)) congruent to S-2 = 0.001, where tau(e) is the entanglement time and S the corresponding order parameter. Finally, we discuss the future prospects of the H-2 FC NMR technique.