The study of exoplanets (planets orbiting stars other than our own sun) has gone from a purely academic conceit to a well-established observational field in only a few decades. While both ground- and space-based observatories continue generating a wealth of exoplanet discoveries and data, future advances in this field will most likely come from dedicated, space observatories that can directly image and spectroscopically characterize new and known exoplanets. The design of such missions, and analysis of the data they are likely to produce, both require probabilistically modeling the, only partially observed, population of exoplanets. In this talk, I will outline the techniques being used to analyze and optimize planned missions, and discuss the inference problem associated with the analysis of current and future exoplanet data sets.