We report on recently published experimental studies on spin sum rules, namely the generalized Gerasimov-Drell-Hearn, Bjorken, Burkhardt-Cottingham, Schwinger, and generalized spin polarizability sum rules. The data were taken at Jefferson Lab in Halls A and B by experiments E97-110 and EG4, respectively. They covered the very low $Q^2$ domain, down to $Q^2$$\simeq$0.02~GeV$^2$, where Chiral Effective Field Theory ($\chi$EFT) predictions should be valid. While some of the obervables agree with the state-of-the-art $\chi$EFT predictions, others are in tensions, including the Longitudinal-Transverse interference polarizability $\delta_{\rm LT}^n(Q^2)$ for which $\chi$EFT prediction was expected to be robust. This suggests that $\chi$EFT does not yet consistently describes nucleon spin observables, even in the very low $Q^2$ domain covered by the experiments.