New neutron-optics effects, which were predicted and discovered quite recently in noncentrosymmetric crystals and which can be used to study the fundamental properties of the neutron, are discussed. In particular, strong electric fields of strength up to 10⁸ or 10⁹ V/cm may act in such crystals on the neutron, and this provides new possibilities for measuring the neutron electric dipole moment (EDM) by the crystal-diffraction method. It also becomes possible to perform searches for pseudomagnetic forces acting on neutrons and violating CP invariance. For the range of such forces that satisfies the condition λ _A < 10^-5 cm, the best constraints on the product of the scalar and pseudoscalar coupling constants have already been obtained for the interaction induced by the exchange of a light pseudoscalar (axion-like) particle. The present-day status and prospects of neutron-optics crystal-diffraction experiments aimed at searches for the neutron EDM and pseudomagnetic forces are considered.