Recent and planned spacecraft exploration of the planets and moons of our solar system have greatly increased interest in atmospheric escape. The Cassini spacecraft is currently improving our understanding of the upper atmosphere of Saturn's large moon Titan, in 2014 the Maven spacecraft will begin to orbit Mars to study its upper atmosphere and atmospheric loss, and in 2015 the New Horizons spacecraft will have a close flyby encounter with Pluto. My motivation has been to produce an accurate model of Pluto's atmosphere, which includes atmospheric loss by escape. The results will be both predictive for and tested against data obtained during the New Horizon encounter. By accurately describing the present loss rates, one can hope to eventually be able to extrapolate back in time in order to describe the long-term evolution of Pluto's atmosphere. Doing this accurately for a planet for which we will have in situ spacecraft data will then guide our ability to model atmospheres for a large number of exoplanets observed orbiting other stars for which there is only remote sensing data.Constraints on Pluto's atmosphere have been obtained through modeling and a few stellar occultation events in the last few decades. These have set a surface pressure range of 6.5-24 microbar of the primarily nitrogen atmosphere, with a methane mixing ratio of ~0.5%. Carbon monoxide has been detected as a trace species out to ~4 planetary radii, suggesting an atmosphere that is much more extended than predicted. Typically hydrodynamic models have been applied to describe escape from planetary bodies such as Pluto and Titan. Such models require solving the fluid equations out to very large distances from the planet in order to enforce boundary conditions. However, it is known ii through molecular kinetic simulations that at some finite distance above the surface the fluid equations fail to describe the gas properties accurately as the atmosphere transitions into the largely collisionless exosphere. To accurately capture the nature of the escape and structure of Pluto's thermosphere and exosphere, I have developed a model of Pluto's upper atmosphere by connecting a fluid model, using radiative heating models relevant for the thermosphere and stratosphere, to a molecular kinetic model. Using this hybrid model I have shown that the atmosphere is much more extended than previously predicted and the escape is not supersonic, as in comet or stellar atmospheres. Rather, it is closer to the evaporative Jeans model of escape.Pluto's lower atmosphere or upper atmosphere have typically been modeled separately, without considering the interactions between these two regimes. Therefore, Ihave developed a self-consistent model of Pluto's full atmosphere, including both the stratospheric radiative heating and cooling that prevail in the lower atmosphere, as well as the UV heating and the cooling by atmospheric escape. These reach a sensitive balance in the upper atmosphere. The stratospheric processes included non-LTE IR radiative heating and cooli...