This thesis presents a search for trans-Neptunian objects (TNOs) using data from the Dark Energy Survey. This population of minor bodies orbiting past Neptune is a relic of the formation history of the Solar System, with the current observed orbital distribution of these planetesimals bearing signatures of large-scale changes in the positions of the giant planets. The Dark Energy Survey (DES) covered $5000\deg^2$ of the sourthern sky in the $grizY$ optical/NIR filter sets between 2013-2019, and the absence of repeated observations in a span of few hours, as typically employed by TNO surveys, makes the search process challenging. To accomplish this, I present new techniques to identify moving objects in catalogs coming from single-epoch images, techniques for linking orbits in a temporally sparse catalog, and a “sub-threshold significance” test, where the object is demanded to be detectable in a stack of the exposures in which the orbit indicates an object should be present, but was not individually detected. The search of the first four years of DES, corresponding to $60,000$ exposures and 22 million transients, yielded 316 validates TNOs, with 50% completeness estimated at $m_r \approx 23.3$ for objects at distances $30 \lesssim d \lesssim 2000 , \au$. The search over the full six years ($80,000$ exposures, 108 million transients) benefits from not only the two additional years of data, but from an optimized detection pipeline capable of finding fainter sources in the same images. This complete search yieleded 769, with 50% completeness at $m_r \approx 23.8$. I also present software for simulation of DES discoveries given a hypothetical TNO population, enabling statistical comparisons of hypothesis to the observed DES data. I also present a test of azimuthal isotropy for the population of extreme'' TNOs ($a > 150\au$, $q > 30\au$) for evidence of gravitational perturbations from an unseen super-Earth in a distant orbit. By rotating the orbits of the detected eTNOs, I construct a synthetic population that reproduces the observed eTNOs in the orbital parameters $a$, $e$, $i$ and absolute magnitude $H$, and that is uniform in $\{\Omega, \omega,\mathcal{M}\}$. I show that the DES eTNOs are consistent with azimuthal isotropy, and thus do not require the existence of a distant Planet 9''.