The rotatory power of a crystal can be modified in the presence of an external force, due to changes of the optical spatial dispersion tensor. In first order, such changes are linear in the applied force, and they must conform with the force-free crystal symmetry, for weak forces. The behavior of the applied force under time reversal should also be considered, since a time-antisymmetric force will modify the axial character of the gyration tensor. In particular, application of an electric field will lead to the so called electro-optical activity (EOA), i.e., rotation of the plane of polarization linearly with the field. Modulation of the applied field will accordingly lead to modulation of the plane of polarization. It is shown that EOA can be separated from the electro-optic effect, birefringence and natural optical activity, by apprpriate choice of crystal class and optical geometry. Similar effects due to a magnetic field have been identified as magneto-spatial effects or magneto-optical activity (MOA). Their relation to the well-known Faraday effect is discussed. Other possibilities are also presented, including stress effects, pressure and temperature effects. The acoustical analog of these effects is also introduced, as well as the possibility of rotational effects, i.e., effects arising from the antisymmetric (rota-tional) part of a shear elastic wave. By using simple group-theoretical arguments, it is shown that the component array of the higher-rank tensors which describe the above non-linear phenomena can, in most cases, be obtained from well-known tensors of crystal physics by inspection. Specific examples are given.