This paper describes the addition of Collision-Induced Absorption (CIA) into the HITRAN compilation. The data from different experimental and theoretical sources have been cast into a consistent format and formalism. The implementation of these new spectral data into the HITRAN database is invaluable for modeling and interpreting spectra of telluric and other planetary atmospheres as well as stellar atmospheres. In this implementation for HITRAN, CIAs of N2, H2, O2, CO2, and CH4 due to various collisionally interacting atoms or molecules are presented. Some CIA spectra are given over an extended range of frequencies, including several H2 overtone bands that are dipole-forbidden in the non-interacting molecules. Temperatures from tens to thousands of Kelvin are considered, as required, for example, in astrophysical analyses of objects, including cool white dwarfs, brown dwarfs, M dwarfs, cool main sequence stars, solar and extra-solar planets, and the formation of so-called first stars.