Massive black holes populate the centers of today's galaxies, including the Milky Way, and shone as quasars in the past; the massive black holes that we detect now in nearby bulges are the remnants of this fiery past. The masses of black holes in local galaxies also define clear correlations with the properties of their hosts, showing that the growth of black holes is intimately linked to the one of their hosts, however, little is known about how they form and interact with their hosts in different environments, especially in at early cosmic epochs. We propose to undertake a theoretical investigation on the formation of massive black holes and their growth inside galaxies using cosmological hydrodynamical simulations and semi analytical models. Using numerical simulations we can explore out-of-equilibrium conditions that cannot be studied analytically, while at the same time analytical models guide the simulations we run. We will use semi-analytical models to create statistical samples in an inexpensive way. The simulations will follow the evolution of the galaxy+black hole system from the epoch of black hole formation to today, in different types of galaxies. We will also explore the evolution of massive black holes during galaxy mergers, which in Cold Dark Matter cosmologies are an integral part of galaxy evolution. The simulations provide information on the evolution of MBHs, that we will parameterize into our semi-analytical models to calculate properties of quasars at different redshifts and wavebands that can be directly compared to observational samples. Observational predictions, such as luminosity functions, redshift distributions, mass functions, and merger rates will be assessed by taking into consideration both currently available facilities and planned new technology.