Electro-optically switchable photonic components based on zenithal bistable liquid-crystal gratings are designed and theoretically investigated. By properly selecting the material and geometrical parameters, we demonstrate that such gratings can operate as switchable beam splitters, beam steerers, quarter-wave plates, and narrowband guided-mode resonant filters. The switching dynamics of the proposed components are also investigated by employing a tensorial formulation for the liquid-crystal orientation problem, which is coupled with the lightwave propagation studies in a multiphysics environment based on the finite-element method.