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 first systems to be studied in the search for CP-violation is the electric dipole moment (EDM) of the neutron. The contribution to the neutron EDM coming from the SM is several orders of magnitudes smaller than the current experimental bound, thus providing a unique background-free window for potential discovery of physics Beyond the Standard Model (BSM).
After a brief summary of the current status for experimental searches of a neutron EDM, I describe the different CP-violating sources and the role played by lattice QCD in constraining the corresponding couplings. I present the difficulties of a calculation of the CP-violating hadronic matrix elements, and then proceed detailing recent results obtained, with my collaborators, with a specific focus on the main theoretical and numerical tool used: the gradient flow. I conclude with near-term goals, challenges and an optimistic view into the future.