Today, we have confidence to say that the discovery of borate series NLO crystals is inseparable from the theoretical understanding of the relationship between the macroscopic NLO and LO properties of the NLO crystals and their microscopic structures. If we had not done a lot of calculations for SHG coefficients of the known NLO crystals and suggested the anionic group theory from the mid-1960s to the end of 1970s, it was nearly impossible to discover the borate NLO crystals in the 1980s. Therefore, this chapter describes the basic concepts and an approximation calculation method for the anionic group theory of NLO effect in crystals, and furthermore, use the model to elucidate the relationship between the macroscopic NLO and LO properties of NLO crystals and their microscopic structures, anionic group structures in particular. Moreover, we have also employed the first-principles method to study the NLO effects and elucidated their microscopic structural origins. On the basis of the theoretical understanding, the processes leading to the discovery of the borate series NLO crystals are further described.In Section 2.1, the basic concepts and calculation method of the anionic group theory of NLO effects in crystals are described with emphasis on the basic idea and the degree of approximation of the theory. In Section 2.2, several typical examples of the principal NLO crystals are given to explain that the major structural units of the NLO crystals to produce SHG effect on the crystals are certainly anionic groups and the contributions of cations in the crystals to the SHG effect can be ignored in the first approximation. In Section 2.3, a DV-SCM-X a localized cluster calculation method is employed to calculate the energy-level structure of the anionic groups in the NLO crystals. From the calculations one can understand the relationship between the energy-level structure of the anionic groups and absorption edge of the NLO crystals. The understanding is very helpful for the molecular engineering approach to search for UV and deep-UV NLO crystals. In Section 2.4, a first-principles calculation method with a plane wave pseudopotential (PWPP) total energy package is used to calculate the refractive indices, SHG coefficients of the NLO crystals, and then a realspace atom-cutting technique is employed to analyze the effect of cations on the SHG coefficients in the NLO crystals and determine the approximation degree of the anionic group theory. In Section 2.5, a computer-assisted molecular design system is introduced, in which the theoretical calculations and experimental methods are Nonlinear Optical Borate Crystals: Principles and Applications, First Edition.