The inevitable galaxy mergers and the existence of massive black holes (>1e5 Msun) at the centre of most galaxies suggests that galaxies may harbour more than one MBH. After a galaxy merger, two MBHs can eventually get sufficiently close to interact gravitationally and form a massive black hole binary (MBHB). According to general relativity, MBHBs emit gravitational waves (GWs) at different frequencies depending on their masses, and separations. Pulsar Timing Array (PTA) experiments target the nHz regime, and recently reported strong evidence of an unexpected loud stochastic GW background produced most likely by a population of >1e8 Msun MBHBs. The future GW space telescope Laser Interferometer Space Antenna (LISA, to be launched in 2034) targets a complementary window, detecting MBHBs of 1e4-1e7 Msun emitting GWs at mHz. The detection of MBHBs systems will be crucial, as their properties and demographics can provide, for the very first time, tight constraints on the formation and evolution of MBHs. Furthermore, the joint detection of these systems across the GW and electromagnetic spectrum will open a new era of multimessenger astronomy. In this talk, I will present the properties and hosts of the MBHBs detected by the PTA and LISA experiments, as well as the challenges associated with using them in multimessenger studies. To this end, I will introduce the L-Galaxies semi-analytical model, a code that encompasses all the relevant physical processes governing the assembly of galaxies, MBHs, and MBHBs, while coupling them with the dark matter merger trees derived from N-body cosmological simulations.