Over the past 2–3 decades our understanding of the outer solar system’s history and current state has evolved dramatically. It is now generally accepted that the orbits of the known giant planets have changed significantly over the last 4.5 Gyrs, and it has recently been proposed that an additional, still undiscovered giant planet orbits at several hundred AU from the Sun. These ideas have primarily been spurred by the discoveries of thousands of small icy bodies called trans-Neptunian objects (TNOs) as well as advances in numerical models of orbital dynamics. Here I will review recent work I and others have undertaken using numerical simulations in concert with catalogs of observed TNOs to constrain the outer solar system’s current orbital architecture and past evolution. In particular, I will focus on highly inclined TNOs whose orbits do not currently approach the known planets. We find that such TNOs can trace Neptune’s past orbital evolution and are sensitive to the presence of a distant, undetected planet.