There is a strong correlation between chemical shifts and local structure. In proteins, this makes it possible to derive secondary structure elements and dihedral φ and ψ angles from chemical shifts.

A useful starting point is the so-called ‘secondary chemical shift’, defined as:

Δδ = δ_observed – δ_{random coil}

The secondary chemical shift is dependent on the protein secondary structure. Cα atoms in α-helices, for example, will tend to have positive secondary chemical shifts and Cα atoms in β-strands will tend to have negative secondary chemical shifts. The behaviour for Cβ atoms is exactly opposite to that of Cα atoms – in β-strands mainly positive secondary chemical shifts are observed and in α-helices mainly negative ones. The chemical shifts of Hα H^N, N^H and C’ chemical shifts are also linked to the secondary structure, though not all as strongly as the Cα and Cβ atoms. These observations initially lead to chemical shift indexing, in which you look for patterns of up- or downfield shifted atoms along the protein sequence in order to identify stretches of α-helix or β-strand (Wishart et al. 1992 and 1994).

The Ramachandran plot (a plot of the φ vs ψ torsion angles in proteins) shows that the secondary structure of a protein is the result of consecutive residues having similar φ and ψ torsion angles, with one area of the plot being linked to α-helices and another to β-strands. It is thus possible to derive not only the secondary structure from chemical shifts, but also the approximate dihedral angles. Most methods for this use databases of high-resolution protein structures whose chemical shifts are known. A combination of matching the sequence and backbone (and Cβ) chemical shifts to those in the database and machine learning methods or Bayesian statistics are then used to derive ranges for the φ and ψ torsion angles. Several programs which predict dihedral angles from chemical shifts are listed on the software page.

References:
D.S. Wishart, B.D. Sykes and F.M. Richards (1992) Biochemistry 31 164-1651. (Link to Article)
D.S. Wishart and B.D. Sykes (1994) J. Biomol. NMR 4 171-180 (Link to Article)