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 order 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). Beside all the CP-violating effective operators describing the contributions from BSM, the neutron EDM can potentially be induced by the strong CP-violating theta term.

After a brief summary of the current status for experimental searches of a neutron EDM, I describe the different CP-violating sources and the challenges of a lattice QCD calculation of the corresponding hadronic matrix elements. I then proceed detailing recent results obtained, with my collaborators, on the neutron EDM with a specific focus on the the main theoretical and numerical tool used: the gradient flow. I conclude with near-term goals, challenges and an optimistic view into the future.