Habitability is a measure of an environments potential to support life, and a habitable exoplanet supports liquid water on its surface. However, a planets success in maintaining liquid water on its surface is the end result of a complex set of interactions between planetary, stellar, planetary system and even Galactic characteristics and processes, operating over the planets lifetime. In this chapter, we describe how we can now determine which exoplanets are most likely to be terrestrial, and the research needed to help define the habitable zone under different assumptions and planetary conditions. We then move beyond the habitable zone concept to explore a new framework that looks at far more characteristics and processes, and provide a comprehensive survey of their impacts on a planets ability to acquire and maintain habitability over time. We are now entering an exciting era of terrestiral exoplanet atmospheric characterization, where initial observations to characterize planetary composition and constrain atmospheres is already underway, with more powerful observing capabilities planned for the near and far future. Understanding the processes that affect the habitability of a planet will guide us in discovering habitable, and potentially inhabited, planets.
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