Halogen bonding (XB) is a type of noncovalent interaction between a halogen atom X in one molecule and a negative site in another. X can be chlorine, bromine or iodine. The strength of the interaction increases in the order Cl<Br<I. After a brief review of experimental evidence relating to halogen bonding, we present an explanation for its occurrence in terms of a region of positive electrostatic potential that is present on the outermost portions of some covalently-bonded halogen atoms. The existence and magnitude of this positive region, which we call the sigma-hole, depends upon the relative electron-attracting powers of X and the remainder of its molecule, as well as the degree of sp hybridization of the s unshared electrons of X. The high electronegativity of fluorine and its tendency to undergo significant sp hybridization account for its failure to halogen bond. Some computed XB interaction energies are presented and discussed. Mention is also made of the importance of halogen bonding in biological systems and processes, and in crystal engineering.