The Trinity Observatory is a proposed UHE-neutrino detector with a core-energy range of $10^6$-$10^{10}$ GeV, bridging the observational gap between IceCube and UHE radio detectors. Trinity is a system of $60\times5$-degree wide field-of-view air-shower imaging telescopes that detect Earth-skimming tau neutrinos from mountain tops. Trinity's primary science objectives are the extension of the IceCube measured neutrino flux to ultrahigh energies and the detection of cosmogenic neutrinos. Over a ten-year observation period, Trinity will detect about 60 diffuse UHE neutrinos if the astrophysical neutrino spectrum does not turn over. Trinity will provide critical measurements to study flavor physics and neutrino cross-sections at energies that are out of reach for accelerators. I present the project's status focusing on the Trinity Demonstrator, a one square meter air-shower imaging telescope we deployed on Frisco Peak, Utah, in July 2023. We the Demonstrator we aim to demonstrate the technology and understand potential backgrounds. In addition, I discuss the discovery potential of diffuse and source UHE neutrinos with the Demonstrator, one Trinity telescope, and the completed system.