Tabulated nuclear magnetic dipole moments from NMR experiment contain a systematic error related to the inaccurate diamagnetic correction, which was historically used for their derivation. In the lecture, I will survey our long-term effort [1,2] to rederive accurate nuclear dipole moments, using ab initio calculations of NMR shielding constants, which replace obsolete diamagnetic corrections. Nuclear magnetic dipole moments of 10B and 11B nuclei will be discussed as an example of gas-phase NMR approach . 209Bi nuclear magnetic dipole moment  will be discussed as an example of NMR shielding calculations for heavy atoms. Finally, new ab initio NMR shielding calculations for sodium ion in aqueous complexes will be presented. New value of 23Na magnetic moment provides an accurate and reliable reference magnetic moment for 26Na nucleus measured by beta-NMR technique at ISOLDE, allowing rederivation of 26Na magnetic moment with relative accuracy of few ppm .
 A. Antusek, K. Jackowski, M. Jaszunski, W. Makulski, and M. Wilczek, Chem. Phys. Lett. 411, 111 (2005)
 M. Jaszunski, A. Antusek, P. Garbacz, K. Jackowski, W. Makulski, and M. Wilczek, Progr. Nucl. Magn. Reson. Spectrosc. 67, 49 (2012).
 K. Jackowski, W. Makulski, A. Szyprowska, A. Antusek, M. Jaszunski, J. Juselius, J. Chem. Phys., 130, 044309 (2009)
 A. Antusek, M. Repisky, M. Jaszunski, K. Jackowski, W. Makulski, and M. Misiak, Phys. Rev. A 98, 052509 (2018).
 to be published