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Second-harmonic generation (SHG) in magnetically ordered crystals is reviewed. The symmetry of such crystals is determined by the arrangement of both the charges and the spins, so their contributions to the crystallographic and the magnetic structures, respectively, must be distinguished. Magnetic SHG is introduced as a probe for magnetic structures and sublattice interactions. The specific degrees of optical experiments - including spectral, spatial, and temporal resolution - lead to the observation of novel physical effects that cannot be revealed by other techniques of probing magnetism. These include local or hidden phase transitions, interacting magnetized and polarized sublattices and domain walls, and magnetic interfaces. SHG in various centrosymmetric and noncentrosymmetric crystal classes of antiferromagnetic oxides such as Cr2O3, hexagonal RMnO3(R=Sc,Y,In,Ho-Lu), magnetic garnet films …