The habitability of the surface of any planet is determined by a complex evolution of its interior, surface, and atmosphere. The electromagnetic and particle radiation of stars drive thermal, chemical, and physical alteration of planetary atmospheres, including escape. Many known extrasolar planets experience vastly different stellar environments than those in our solar system: It is crucial to understand the broad range of processes that lead to atmospheric escape and evolution under a wide range of conditions if we are to assess the habitability of worlds around other stars. One problem encountered between the planetary and the astrophysics communities is a lack of common language for describing escape processes. Each community has customary approximations that may be questioned by the other, such as the hypothesis of H‐dominated thermosphere for astrophysicists or the Sun‐like nature of the stars for planetary scientists. Since exoplanets are becoming one of the main targets for the detection of life, a common set of definitions and hypotheses are required. We review the different escape mechanisms proposed for the evolution of planetary and exoplanetary atmospheres. We propose a common definition for the different escape mechanisms, and we show the important parameters to take into account when evaluating the escape at a planet in time. We show that the paradigm of the magnetic field as an atmospheric shield should be changed and that recent work on the history of Xenon in Earth's atmosphere gives an elegant explanation to its enrichment in heavier isotopes: the so‐called Xenon paradox. Plain Language Summary In addition to having the right surface temperature, a planet needs an atmosphere to keep surface liquid water stable. Although many planets have been found that may lie in the right temperature range, the existence of an atmosphere is not guaranteed. In particular, for planets that are kept warm by being close to dim stars, there are a number of ways that the star may remove a planetary atmosphere. These atmospheric escape processes depend on the behavior of the star as well as the nature of the planet, including the presence of a planetary magnetic field. Under certain conditions, a magnetic field can protect a planet's atmosphere from the loss due to the direct impact of the stellar wind, but it may actually enhance total atmospheric loss by connecting to the highly variable magnetic field of the stellar wind. These enhancements happen especially for planets close to dim stars. We review the complete range of atmospheric loss processes driven by interaction between a planet and a star to aid in the identification of planets that are both the correct temperature for liquid water and that have a chance of maintaining an atmosphere over long periods of time. Key Points The different escape processes at planets and exoplanets are reviewed along with their mathematical formulation The major parameters for each escape processes are described; some escape processes negligible in the solar system may be major source at exoplanets, or for the early solar system A magnetic field should not be a priori considered as a protection for the atmosphere