Periodic optical systems, such as photonic crystals and optical metamaterials, can localize high-density electromagnetic field energy at subwavelength scales and obtain extremely small mode volumes, so they have great application potential in the field of light manipulation. In recent years, a strong interaction between light and matter in periodic optical systems has been discovered, which is called Bound States in Continuum (BIC). Optics BICs are special electromagnetic eigenstates whose frequencies lie in the radiation continuum but are completely localized, and have shown interesting physics and rich application scenarios. This paper systematically reviews the classification and theory of BICs in periodic optical systems, and summarizes their basic physical properties and the latest application development. BICs in periodic optical systems are injecting new impetus into the fields of integrated optics, information optics, bio-optics, topological optics, and nonlinear optics.