The σ-hole and π-hole are the regions with positive surface electrostatic potential on the molecule entity; the former specifically refers to the positive region of a molecular entity along extension of the Y-Ge/P/Se/X covalent σ-bond (Y = electron-rich group; Ge/P/Se/X = Groups IV-VII), while the latter refers to the positive region in the direction perpendicular to the σ-framework of the molecular entity. The directional noncovalent interactions between the σ-hole or π-hole and the negative or electron-rich sites are named σ-hole bond or π-hole bond, respectively. The contributions from electrostatic, charge transfer, and other terms or Coulombic interaction to the σ-hole bond and π-hole bond were reviewed first followed by a brief discussion on the interplay between the σ-hole bond and the π-hole bond as well as application of the two types of noncovalent interactions in the field of anion recognition. It is expected that this review could stimulate further development of the σ-hole bond and π-hole bond in theoretical exploration and practical application in the future.