NMR chemical shifts have an extremely high information content on the behaviour of macromolecules, owing to their non-trivial dependence on myriads of structural and environmental factors. Although such complex dependence creates an initial barrier for their use for the characterisation of the structures of protein and nucleic acids, recent developments in prediction methodologies and their successful implementation in resolving the structures of these molecules have clearly demonstrated that such barrier can be crossed. Furthermore, the significance of chemical shifts as useful observables in their own right has been substantially increased since the development of the NMR techniques to study low populated "excited" states of biomolecules. This work is aimed at increasing our understanding of the multiple factors that affect chemical shifts in proteins and nucleic acids, and at developing high-quality chemical shift predictors for atom types that so far have largely escaped the attention in chemical shift restrained molecular dynamics simulations. A general approach is developed to optimise the models for structure-based chemical shift prediction, which is then used to construct CH3Shift and ArShift chemical shift predictors for the nuclei of protein side-chain methyl and aromatic moieties. These results have the potential of making a significant impact in structural biology, in particular when taking into account the advent of recent techniques for specific isotope labelling of protein side-chain atoms, which make large biomolecules accessible to NMR techniques. Through their incorporation as restraints in molecular dynamics simulations, the chemical shifts predicted by the approach described in this work create the opportunity of studying the structure and dynamics of proteins in a wide range of native and non-native states in order to characterise the mechanisms underlying the function and dysfunction of these molecules.