A reliable representation of local interactions is critical for the accuracy of modeling protein structure and dynamics at both the all-atom and coarse-grained levels. The development of local (mainly torsional) potentials was focused on careful parametrization of the predetermined (usually Fourier) formulas rather than on their physics-based derivation. In this Perspective we discuss the state-of-the-art methods for modeling local interactions, including the scale-consistent theory developed in our laboratory, which implies that the coarse-grained torsional potentials inseparably depend on the virtual-bond angles adjacent to a given dihedral and that multitorsional terms should be considered. We extend the treatment to split the residue-based torsional potentials into the site-based regular and improper torsional potentials. These considerations are illustrated with the revised torsional potentials and improper-torsional potentials involving the l-alanine residue and the improper-torsional potential corresponding to serine-residue enantiomerization. Applications of the new approach in coarse-grained modeling and revising all-atom force fields are discussed.