Pairs of accreting supermassive black holes (SMBHs), known as dual active galactic nuclei (AGN), and the generation of gravitational waves (GWs) from the inspiral and coalescence of SMBHs are two faces of the same coin. The SMBHs that, by coalescing, generate GWs detectable by the Laser Interferometer Space Antenna (LISA) are the same systems which, millions or billions of years earlier, were potentially both accreting gas at the centre of a galactic merger remnant and producing a dual AGN, akin to the few systems we currently observe via electromagnetic (EM) probes. Connecting these two physical events is paramount to understanding (i) how the large scale structure of the Universe evolved, (ii) how SMBHs and their host galaxies co-evolve, and (iii) how SMBH accretion and AGN feedback work. To do so, we need to perform high-resolution numerical simulations that model a huge variety of astrophysical systems and processes, compare our results to current EM observations, and be ready to interpret the signals that will come from evolved EM probes (e.g. ATHENA) and, soon, from LISA. In this talk, I will show that both SMBH pairing and dual AGN activity can depend significantly on a wide assortment of astrophysical parameters, including the mass ratio between two merging galaxies, the occurrence of gas instabilities, and the dark matter content of the interacting systems, to name a few, making the field of multi-messenger astrophysics both challenging and exciting.