The study of the atmospheres of exoplanets has evolved into a frontier topic in astronomy and astrophysics. In principle, these atmospheres encode information on the formation history of exoplanets, their gaseous chemical inventory, and whether they are habitable and/or inhabitable. In practice, there are a series of unsolved theoretical problems that need to be overcome before the promise of exoplanetary atmospheres is fulfilled. In this colloquium, I will review a selected subset of these problems, some of which are active topics of research within my group and research center. As a prelude, I will perform a concise, theorist’s review of the landscape of current and future observations, both from the ground and space. I will then discuss the following 5 problems: degeneracies in transmission spectra, cloudiness, 1D versus 3D models, geochemical cycles and biosignature gases. I will end by performing a concise, executive review of my new textbook (“Exoplanetary Atmospheres: Theoretical Concepts and Foundations”) by Princeton University Press. (The first student who comes up to me after the colloquium and demonstrates that he/she is a student will receive a free copy.)