Nuclear magnetic resonance (NMR) has played an extremely important role in solid-state research ever since its discovery. Variable-temperature NMR is often employed to investigate the static and dynamic properties of materials. However, performing NMR at very low cryogenic temperatures requires careful design of the experiment. In this contribution, we first address some of the “nuts and bolts” of these experiments, i.e., the description of the cryogenic equipment and the NMR probe designs. The range of motivations for performing NMR experiments at very low temperatures is extremely broad. Here we illustrate two applications of low-temperature NMR for the studies of complex molecular dynamics and for the discoveries of novel states of matter in low-dimensional magnetic systems. Specifically, we address (i) the dynamics of fullerene C60 molecules in pristine as well as in intercalated C60 phases, (ii) magnetism in quasi-one-dimensional antiferromagnets CsO2 and TiPO4 where Tomonaga–Luttinger-liquid physics and the spin-Peierls transitions were discovered, and (iii) low-temperature- and high-field-induced novel phases of two-dimensional dimer copper oxides, SrCu2(BO3)2 and BaCuSi2O6. We present the theoretical formalism, as well as examples of measurements, aiming at providing an introduction into the application of low-temperature NMR techniques.