Imaging Atmospheric Cherenkov Telescope arrays allow us to probe the gamma-ray sky from tens of GeV up to hundreds of TeV. They operate by stereoscopically imaging the Cherenkov light generated when an astrophysical gamma-ray interacts with Earth's atmosphere. In order to reject charged cosmic ray events, and to reconstruct the direction and energy of the incident gamma-ray, machine learning methods are used in combination with parametric descriptions of the detected images. One potential means of improving performance for the next-generation Cherenkov Telescope Array (CTA) is to apply new deep learning methods in place of these parametric techniques. In this thesis, we explore the complexity of deploying deep learning methods, first consid...