High-resolution NMR spectroscopy is the leading method for determining nuclear magnetic moments. It is designed to measure stable nuclei that can be investigated in macroscopic samples. In this work, we discuss the progress in research into light nuclei from the first three periods of the Periodic Table and several selected heavy nuclides. New 1H and 3He nuclei using the Penning trap method are also considered. Both nuclei can be used as references in gaseous mixtures. Gas-phase NMR spectroscopy enables precise measurements of the frequencies and shielding constants of isolated single molecules. They can be used to determine new, accurate nuclear magnetic moments of nuclides in stable, gaseous substances. Particular attention is paid to the importance of diamagnetic corrections for obtaining accurate results. Finding precise diamagnetic corrections - shielding factors, even in the case of light nuclei in molecules, is a big challenge. Up to now, nuclear moments have been obtained primarily from experimental results. The theoretical approach is mostly unable to predict these values accurately. Some remarks are also made on pure theoretical treatments of nuclear moments.