Exoplanetary atmospheric retrieval refers to the inference of atmospheric properties of an exoplanet given an observed spectrum. The atmospheric properties include the chemical compositions, temperature profiles, clouds/hazes, and energy circulation. These properties, in turn, can provide key insights into the atmospheric physicochemical processes of exoplanets as well as their formation mechanisms. Major advancements in atmospheric retrieval have been made in the last decade, thanks to a combination of state-of-the-art spectroscopic observations and advanced atmospheric modeling and statistical inference methods. These developments have already resulted in key constraints on the atmospheric H2O abundances, temperature profiles, and other properties for several exoplanets. Upcoming facilities such as the JWST will further advance this area. The present chapter is a pedagogical review of this exciting frontier of exoplanetary science. The principles of atmospheric retrievals of exoplanets are discussed in detail, including parametric models and statistical inference methods, along with a review of key results in the field. Some of the main challenges in retrievals with current observations are discussed along with new directions and the future landscape.

30 pages, 3 figures, Published in Springer Handbook of Exoplanets