During the last three decades, it has become increasingly clear that atmospheric modelling and remote sounding of the atmosphere from space, to name just two important application areas, are affected by non-equilibrium processes which have not been incorporated into traditional radiative transfer calculations. These processes, dubbed "non-LTE", are therefore the subject of growing interest among scholars and researchers dealing with the upper atmosphere. This book provides a comprehensive and "global" description of non-LTE infrared emissions in the atmosphere of the Earth and other planets, starting with the theoretical foundations and progressing to the most important applications. Besides giving an introduction to this complex subject, it is a guide to the state-of-the-art in incorporating non-LTE processes into radiative transfer algorithms and computer models of the atmosphere. Numerous examples are presented of the application of these methods to: atmospheric remote sensing, atmospheric energy budget (cooling and heating rate) calculations, and atmospheres other than the Earth's.