Unlocking Gravity and Gravitational Waves with Radio Pulsars: Advances and Challenges

Pulsars, the cosmic lighthouses, are strongly self-gravitating objects with core densities significantly exceeding nuclear density. Since the discovery of the Hulse--Taylor pulsar 50 years ago, binary pulsar studies have delivered numerous stringent tests of General Relativity (GR) in the strong-field regime as well as its radiative properties -- gravitational waves (GWs). These systems also enable high-precision neutron star mass measurements, placing tight constraints on the behaviour of matter at extreme densities. In addition, pulsars act as natural detectors for nanohertz GWs, primarily from supermassive black hole binaries, culminating in the first reported evidence of a stochastic GW background in 2023. In this article, I review key milestones in pulsar research and highlight some of contributions from my own work. After a brief overview of the gravity experiments in \S 1, I review the discovery of pulsars -- particularly those in binaries -- and their critical role in gravity experiments (\S 2) that laid the foundation for recent advances. In \S 3, I present the latest efforts on GR tests using the Double Pulsar and a pioneer technique to constrain the dense matter equation of state. \S 4 demonstrates the potential of binary pulsars on testing alternative theories to GR. Advances in nanohertz GW detection with pulsar timing arrays are discussed in \S 5. I outline some of the current challenges in \S 6 and conclude with final remarks in \S 7.