Supermassive black holes (BHs) harboured in the center of galaxies have been confirmed with the discovery of Sagittarius A* in the center of our galaxy, the Milky Way. Recent surveys indicate that BHs of millions of solar masses are common in most local galaxies, but also that some local galaxies could be lacking BHs (e.g. NGC205, M33), or at least hosting low-mass BHs of few thousands solar masses. Conversely, massive BHs under their most luminous form are called quasars, and their luminosity can be up to hundred times the luminosity of an entire galaxy. We observe these quasars in the very early Universe, less than a billion years after the Big Bang. BH formation models therefore need to explain both the low-mass BHs that are observed in low-mass galaxies today, but also the prodigious quasars we see in the early Universe.BH formation is still puzzling today, and many questions need to be addressed: How are BHs created in the early Universe? What is their initial mass? How many BHs grow efficiently? What is the occurrence of BH formation in high redshift galaxies? What is the minimum galaxy mass to host a BH? We have used cosmological hydrodynamical simulations to capture BH formation in the context of galaxy formation and evolution. Simulations offer the advantage of following in time the evolution of galaxies, and the processes related to them, such as star formation, metal enrichment, feedback of supernovae and BHs. We have particularly focused our studies on the three main BH formation models: Pop III remnant, stellar cluster, and direct collapse models.