Pulsars, rapidly-rotating highly-magnetised neutron stars, can serve as useful laboratories for probing aspects of fundamental physics. Binary pulsars, especially those in tight binary systems with massive, compact companions, are useful in testing different theories of gravity, the current paradigm being General Relativity (GR). Additionally, binary pulsars can also be utilised to explore other areas of fundamental physics, such as the behaviour of matter at ultra-high densities and the neutron star moment of inertia. A standout example is PSR J1757-1854, a 21.5-ms pulsar in a highly-eccentric (e=0.61), 4.4-hr orbit around a neutron star companion. This pulsar exhibits some of the most extreme relativistic parameters ever observed in a binary pulsar, reaching a maximum line-of-sight acceleration of close to 700 m/s/s and displaying among the strongest relativistic effects due to gravitational wave damping. To date, five post-Keplerian parameters have been measured in PSR J1757-1854, allowing for three independent tests of gravity to be conducted (of which GR passes all three) and for the component neutron star masses to be separated. The extreme properties of this system (particularly its high eccentricity) are expected to allow for future measurements of Lense-Thirring precession effects (allow for a measurement of the neutron star moment of inertia) and the relativistic deformation of the orbit, both of which remain almost completely unexplored by other binary systems. Although first discovered by the Parkes Radio Telescope in 2016 as part of the High Time Resolution Universe Southern Galactic Plane survey, it is ongoing observations with the Green Bank Telescope (GBT) which have provided the backbone of PSR J1757-1854’s continuing study. The large-bandwidth, high-precision observations afforded by the GBT played a fundamental role in delivering the science derived from the pulsar so far, and will be critical in allowing it to reach its full scientific potential going forward. In this talk I will provide a progress report on the ongoing timing of the system, including a review of the latest mass measurements and gravity tests, with an emphasis towards the future science which this pulsar will make possible
