The second-order nonlinear optical (NLO) crystal materials with the capability of converting the laser frequency, and modulating the amplitude and phase of the laser, are indispensable in practical applications, such as modern manufacturing, laser medical treatment, and communications, as well as in fundamental research. This article provides a brief review of the atom response theory (ART) of nonlinear optical materials developed on the basis of the partial response functional (PRF) method. ART analysis makes it possible to quantitatively evaluate the contribution of individual constituent atoms and orbitals to the second harmonic generation (SHG) response of a nonlinear optical crystal material based on the first principles density functional theory calculations. Besides, a general group division scheme based on physical performance was developed, which provides the conceptual foundation for determining the functional motifs of the SHG effect. In this review, the latest progress of atom response theory and the related new concepts and insights, such as the role of the conduction band, negative atomic contributions, the role of static dipole moment, the overwhelming contribution of non-covalent groups, linear relationships, etc. are explained and elaborated, and some examples for the design of new materials are also given.