Chiral effective-field theory of the nucleon spin structure

I will review the recent chiral EFT calculations of the nucleon (spin) structure functions at low $Q^2$, confronted with the Jefferson Lab measurements. The moments of the structure functions correspond with various polarizabilities, and I will explain why one of them --- $\delta_{LT}$ --- is especially interesting. I will also discuss how the spin structure functions at low $Q$ enter in the atomic calculations of the hyperfine splittings and how they are impacting the ongoing experimental program at PSI (Switzerland) to measure the ground-state hyperfine splitting of muonic hydrogen.