Milkyway@home studies the history of our galaxy by analyzing the stars in the Milky Way galaxy's Galactic Halo. This includes searching for elusive dark matter. This research is done by mapping structures of stars orbiting the Milky Way - many these structures are actually "tidal debris streams," or dwarf galaxies that are being pulled apart by our Galaxy's superior gravitational field. The orbits, shapes, and compositions of these dwarf galaxies provide vital clues to the history of our Galaxy, as well as to the distribution of dark matter.
Additionally, Milkyway@home has recently started developing the "N-body" sub-project, which creates simulated dwarf galaxies and "shoots" them into the Milky Way's gravitational field. We allow the simulated dwarf galaxy's initial conditions to vary until the final simulated dwarf matches what we see in actual halo structures. In other words, we are trying to match dwarf galaxy models to real data, in order to learn more about what is (and what isn't) possible for our Galaxy.
For both projects, we use data from the Sloan Digital Sky Survey(see below)
Here's a visualization by Shane Reilly, showing the Milky Way galaxy (center blue-to-red spiral), a model for the disrupted Sagittarius dwarf galaxy (blue), and an example wedge of SDSS data (yellow).