More than 800 extra-solar planets (exoplanets) have been identified since 1995. Exoplanetary atmosphere and climate are two of the newest areas in exoplanetary science research. The purpose of the present paper is to review the most recent progresses in these areas. Because Earth’s atmosphere and climate are always used as a reference for studies in solar planetary atmospheres and climates, we first briefly introduce basic knowledge of these areas for comparison. We next introduce concepts of habitable zone of stars and habitability of exoplanets. We mainly focus on recent observational, simulation, and theoretical results of physical, chemical, and dynamical properties of exoplanetary atmospheres. Moreover, we introduce possible climate environments of habitable exoplanets around M-type dwarfs.