  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.
