When molecules are placed into an external magnetic field, the response of the electrons leads to an additional induced magnetic field, which gives rise to NMR chemical shifts. It is usually assumed that the induced field is linear in the external field, with the "proportionality constant" being the chemical shielding tensor σ. Under this assumption, chemical shifts are field-independent. For example, one would obtain the same shifts in parts per million (ppm) at 400 MHz or 600 MHz 1 H Larmor frequency. However, at strong enough fields, nonlinear effects become increasingly important. This becomes relevant as commercially available NMR spectrometers continuously move towards higher magnetic fields (currently up to 1.2 GHz 1 H Larmor frequency) because of benefits like higher resolution and sensitivity. In non-commercial contexts, even stronger fields than that have been achieved. A well-known "indirect" 3 effect of magnetic field strength on the measured chemical shifts is due to the non-isotropic averaging of the chemical shielding tensor in solution, which is known as residual chemical shift anistropy. The non-isotropic averaging is caused by partial orientation of the molecules with respect to the external field direction, because some orientations of the molecule have a lower energy than others in the case of an anisotropic magnetic susceptibility tensor. Of course, this effect is larger for paramagnetic molecules, which have intrinsically larger anisotropies. On top of this indirect effect there is the "direct" 3 field dependence caused by a nonlinear response of the induced field to the external field. For diamagnetic molecules, Ramsey theoretically predicted this phenomenon already in 1970 with the introduction of the τ tensor, which describes the part of the induced field that is cubic in the external field (the quadratic part always being identically zero). This was then proven by measurements of fielddependent Co NMR shifts in diamagnetic Co III complexes. Over the years, the effect was theoretically treated by various authors until a recent joint experimental and theoretical study corrected the old values for the Co chemical shifts in the Co(acac) 3 complex by an order of magnitude, and finally reconciled measurements and theoretical predictions.