Exoplanets with substantial Hydrogen/Helium atmospheres have been discovered in abundance, many residing extremely close to their parent stars. The extreme irradiation levels these atmospheres experience causes them to undergo hydrodynamic atmospheric escape. Ongoing atmospheric escape has been observed to be occurring in a few nearby exoplanet systems through transit spectroscopy both for hot Jupiters and lower-mass super-Earths/mini-Neptunes. Detailed hydrodynamic calculations that incorporate radiative transfer and ionization chemistry are now common in one-dimensional models, and multi-dimensional calculations that incorporate magnetic-fields and interactions with the interstellar environment are cutting edge. However, there remains very limited comparison between simulations and observations. While hot Jupiters experience atmospheric escape, the mass-loss rates are not high enough to affect their evolution. However, for lower mass planets atmospheric escape drives and controls their evolution, sculpting the exoplanet population we observe today.

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