The great abundance of exoplanets and the unexpectedly wide range of their bulk properties create a huge realm of possibilities in exoplanet atmospheres. Opportunities for atmospheric characterization of other worlds abound, as well as pitfalls for the unwary. This chapter contains a first foray into exploring the richness of exoplanet atmospheres, with a tour of the exoplanet “spectral zoo.” We then follow the path of light from a star onto an exoplanet and to a distant spectrograph; details about exoplanet atmosphere structure and what happens to light within a planet’s atmosphere will be discussed in other chapters of this volume. We briefly discuss how the light is then affected by the spectrograph and recorded by a detector, resulting in an observed planet spectrum. As will be seen, one of the major challenges for measuring the effects of a planet’s atmosphere in an observed spectrum is disentangling them from effects caused by the instrumentation used to acquire that spectrum. We conclude with a few thoughts on general strategies to overcome observational challenges and harvest the best science from the treasure trove of exoplanets that can and will be studied in the coming decades.