Supermassive black holes from kpc to pc scales

Supermassive black holes mergers emit gravitational waves, which we will detect when LISA is launched. However, the emission of gravitational waves is the end of a billion years story: initially, the two black holes are in the center of their host galaxy, separated by hundreds of kpc, then, hopefully, those galaxies merge and the two black holes meet in the center of this remnant galaxy to finally merge. During this talk, I will begin by reviewing the different things happening to black holes during this long journey. I will then present a new set of cosmological simulations designed to study black holes at high redshift, and show the different implications in the context of LISA.