The fundamentals on non-local thermodynamic equilibrium (non-LTE) in the atmosphere are briefly described as well as for which atmospheric emissions, in which regions and for which instruments (viewing geometry, spectral coverage and resolution), non-LTE processes are more important. The retrieval of atmospheric species from non-LTE infrared emissions and the different options for performing non-LTE retrievals are discussed. The IMK/IAA non-LTE retrieval scheme for inverting atmospheric species from the MIPAS spectra and its application to the retrievals of the CO and NO abundances and non-LTE parameters related to the CO2 levels emitting near 4.3 µm are described. Finally, a non-LTE parameterization of the CO2 4.3 µm daytime outgoing radiation in the nadir view is described and its potential application to low altitude atmospheric temperature sounding from nadir infrared instruments is discussed.