Detecting and Characterizing Exomoons and Exorings (Handbook of Exoplanets, 2nd Edition)

The circumplanetary environments in our Solar System host a stunning array of moon and ring systems. Study of these environs has yielded valuable insights into planetary system formation and evolution, and there is every reason to believe that we will have much to learn from the moons and rings that are likely to exist in exoplanetary systems as well. This has motivated a small but growing number of researchers to investigate questions related to the formation, stability, long-term viability, composition, and observability of these exomoons and exorings. Still, due to a range of significant observational challenges, we remain at a relatively early stage of this work. As a result, we continue to face a number of difficult, unanswered questions, but this also means there are myriad opportunities for fundamental contributions to the field. In this review we will examine a variety of important issues for the astronomical community to consider, with an aim of providing a comprehensive understanding of ongoing efforts to identify and characterize exomoons and exorings, while also increasing interest and engagement. We begin with an overview of what we expect from systems hosting moons and/or rings in terms of their architectures, habitability, and observational signatures. We then highlight the contributions from a variety of works that have been aimed at detecting and characterizing them. We conclude by examining the outlook for finding these objects and discussing a number of ongoing challenges that we will want to overcome in the years ahead.