The observed baryon asymmetry in the universe cannot be reconciled with the current form of the Standard Model (SM) of particle physics. The amount of CP-violation stemming from the Cabibbo-Kobayashi-Maskawa matrix is not sufficient to explain the observed matter-antimatter asymmetry. Historically, one of the initial systems investigated in the search for discrete symmetries violations was the electric dipole moment (EDM) of the neutron. Nowadays, it offers a unique opportunity to discover physics beyond the SM due to its significantly suppressed CP-violating contribution from the SM.
After a brief summary of the current status for experimental searches of a neutron EDM, I delve into the various sources of CP-violation and the computational challenges associated with calculating the corresponding hadronic matrix elements using the lattice as a regulator. I then proceed detailing recent results obtained on the neutron EDM highlighting the primary theoretical and numerical tool employed: the gradient flow. By leveraging this approach, I showcase significant progress made in understanding the neutron EDM. I conclude outlining the near-term objectives, addressing the challenges lying ahead, and providing an optimistic outlook for the future of neutron EDM research.