The second harmonic generation microscope (SHGM) constructs images of intensity distributions of SH waves produced by the interaction of fundamental waves with a polar material. We have developed this nonlinear optical microscope in order to make possible nondestructive, three-dimensional (3D) observations of various kinds of inorganic and organic materials. The SHGM can disclose also inverted domain structures of antiparallel spontaneous polarizations using the interference with the reference SH waves. The observation principle and several applications to structural characterizations of LiNbO3 and LiTaO3 quasi-phase matching devices, domain structure analyses of a relaxor/ferroelectric solid solution Pb(Zn1/3Nb2/3)O3-9%PbTiO3 at the morphotropic phase boundary, development of order parameter in a quantum paraelectric relaxor Li-doped KTaO3, and antiphase polar domain structures of muscle fibers and myofibrils are surveyed by stressing the high effectiveness of the SHGM as a tool of material diagnosis.