When a light beam traveling in one direction in a crystal experiences a different absorption and refractive index compared to the beam traveling in the opposite direction, it is called nonreciprocal directional anisotropy, or simply nonreciprocity. This phenomenon is governed by the fundamental symmetries of crystals under spatial inversion and time reversal symmetries. We will discuss the necessary symmetry conditions for the nonreciprocity of light propagation and of other excitations in solids. Among specific examples, we will consider light propagation, in polar magnetic materials along and opposite the toroidal vector. In this case, a crystal can be completely transparent in one direction and completely opaque in the opposite one – an optical diode. We report a giant optical diode effect in the polar material FeZnMo3O8, where we find more than a 100-fold difference in intensity of light transmitted in the two opposite directions. In addition to the high magnitude of the effect, we show that the effect exists at high temperature in the magnetically disordered state. We will also present a study of the nonreciprocal reflectance of magneto-plasma in semiconductor InSb. This material can be used for the construction of high-performance terahertz isolation devices, as no dominant technology has emerged yet for this application. Room-temperature operation, moderate applied magnetic field, and an unmatched simplicity of design make this material a good candidate for practical terahertz isolators.