Artificial microstructure, due to its ability to trap electromagnetic waves of a specific frequency, which is one of the important platforms to enhance light-matter interactions and manipulate optical fields. Bound states in the continuum (BICs) are located in the continuous radiation region in the spectra, which are an eigenstate completely orthogonal to the radiation continuum in an open wave system. Originating from the destructive interference of waves, BICs can greatly suppress the radiation loss of micro-nano photonic devices, which offer a brand-new solution to optical binding in artificial micro-nanostructures. In this paper, the historical developments of BICs are briefly reviewed. Besides, the advancements and applications of the theoretical models of BICs in different optical artificial micro-nanostructures are emphatically introduced. In conclusion, BICs are expected to boost further progress in optical communications, integrated photonics, and efficient optical field manipulation.