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A planetary atmosphere is the outer gas layer of a planet.Besides its scientific significance among the first and most accessible planetary layers observed from space,it is closely connected with planetary formation and evolution,surface and interior processes,and habitability of planets.Current theories of plan-etary atmospheres were primarily obtained through the studies of eight large planets,Pluto and three large moons(Io,Titan,and Triton)in the Solar System.Outside the Solar System,more than four thousand ex-trasolar planets(exoplanets)and two thousand brown dwarfs have been confirmed in our Galaxy,and their population is rapidly growing.The rich information from these exotic bodies offers a database to test,in a statistical sense,the fundamental theories of planetary climates.Here we review the current knowledge on atmospheres of exoplanets and brown dwarfs from recent observations and theories.This review highlights important regimes and statistical trends in an ensemble of atmospheres as an initial step towards fully char-acterizing diverse substellar atmospheres,that illustrates the underlying principles and critical problems.Insights are obtained through analysis of the dependence of atmospheric characteristics on basic planetary parameters.Dominant processes that influence atmospheric stability,energy transport,temperature,com-position and flow pattern are discussed and elaborated with simple scaling laws.We dedicate this review to Dr.Adam P.Showman(1968-2020)in recognition of his fundamental contribution to the understanding of atmospheric dynamics on giant planets,exoplanets and brown dwarfs.