In astrophysics we are beginning to work with extremely large data sets. However, unlike in most other data-science domains, we have a reasonable handle on the physical processes that generate those data: We have working models that do a fairly good job of describing the quantitative properties of galaxies, stars, and charge-coupled devices. In particular, we have pretty good descriptions of our sources of noise. For these reasons, the most sensitive and accurate measurements being made in astrophysics are made by building highly informed, probabilistic models of the data. I show some examples of scientific discoveries made by modeling data and look to the future, when data sets reach peta-scale and the models have billions of free parameters.