Halogen bonding is a noncovalent interaction that is receiving rapidly increasing attention because of its significance in biological systems and its importance in the design of new materials in a variety of areas, for example, electronics, nonlinear optical activity, and pharmaceuticals. The interactions can be understood in terms of electrostatics/polarization and dispersion; they involve a region of positive electrostatic potential on a covalently bonded halogen and a negative site, such as the lone pair of a Lewis base. The positive potential, labeled a σ hole, is on the extension of the covalent bond to the halogen, which accounts for the characteristic near-linearity of halogen bonding. In many instances, the lateral sides of the halogen have negative electrostatic potentials, allowing it to also interact favorably with positive sites. In this discussion, after looking at some of the experimental observations of halogen bonding, we address the origins of σ holes, the factors that govern the magnitudes of their electrostatic potentials, and the properties of the resulting complexes with negative sites. The relationship of halogen and hydrogen bonding is examined. We also point out that σ-hole interactions are not limited to halogens, but can also involve covalently bonded atoms of Groups IV-VI. Examples of applications in biological/medicinal chemistry and in crystal engineering are mentioned, taking note that halogen bonding can be "tuned" to fit various requirements, that is, strength of interaction, steric factors, and so forth.