Exoplanet searches have uncovered a large population of planets at small orbital separations. Due to the proximity of these planets to their host stars, they receive intense irradiation. This irradiation intensely heats the upper atmospheres of the planets, making them susceptible to undergoing hydrodynamic escape. For small, gas-rich planets, the cumulative effect of this mass loss is thought to be capable of stripping their primordial atmospheres. Evolutionary modelling of this process is used to infer the properties of the planet population at birth. However, the inferred planetary properties are sensitive to modelled escape rates, so accurate escape models are necessary to ensure confidence in any conclusions. Direct observations of atmospheric escape from transiting exoplanets provide an opportunity to test these models. This thesis focuses on modelling hydrodynamic escape, with the specific goal of using these models to interpret observations.