Thousands of exoplanets have been discovered over the past few years. These discoveries were enabled by large and homogeneous space-based time domain surveys of nearby stars, including NASA's Kepler Mission. To push the exoplanet detection threshold to the smallest planets or the longest orbital periods using these data, we combine physical models of exoplanets with data-driven models of the stars and the spacecraft. Scaling these models to be applied to hundreds of thousands of stars with tens of thousands of measurements each poses an interesting technical challenge that we have solved in close interdisciplinary collaboration. In this talk, I will describe the current and future datasets, and the basic problem of exoplanet detection. I will go on to outline the technical challenges and present some of our solutions. Finally, I will discuss how we understand the place of our Solar System in the greater context of the population of planets using these discoveries.