Astronomy is a prime user community for machine learning and probabilistic modeling. There are very large, public data sets (mostly but not entirely digital imaging), there are simple but effective models of many of the most important phenomena (stars, quasars, and galaxies), and there are very good models of telescopes, cameras, and detectors. I will show in detail some examples of problems we were able to solve in astrophysics by bringing probabilistic inference and decision theory to astronomy. I will discuss why many "supervised" methods are not nearly as useful in astronomy as those that involve generative modeling. I hope to leave the audience with real research problems, the solutions to which would be (a) achievable with contemporary machine-learning methods, and at the same time (b) very exciting within the astrophysics community.