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Exomoons remain amongst the most elusive targets in observational astronomy. Nevertheless, these worlds stand to provide an unprecedented window into the formation and evolution of planetary systems. If the Solar System is any guide, we can expect exomoons will be geologically active and diverse, with the potential for hosting volatiles, atmospheres, and even life. Moreover, a thorough understanding of the population and occurrence rates of exomoons will help to place our own Solar System in a galactic context, speaking to the commonality of our own history. And though there are a variety of known pathways for moon formation, the discovery of exomoons may yet reveal heretofore unanticipated system architectures that defy easy explanation, thereby enriching our theoretical understanding of system formation. In this talk I will present my dissertation research, focusing first on a population study of exomoons in the Kepler data. I will then highlight my work related to the HST observation of Kepler-1625b, potentially the first transiting exomoon discovery. Finally, I will discuss my ongoing efforts to detect candidate exomoon signals in the Kepler data through deep learning, and argue that both targeted and survey observations have a role to play in finding exomoons going forward.