Theoretical Modelling of Early Massive Black Holes

These notes review theoretical models of massive black hole formation, growth and observables. They start with a brief summary of basic properties of massive black hole properties. The current view on massive black holes and active galactic nuclei at high redshift is then summarized, highlighting the JWST ``revolution'' and the questions raised by the recent observations. The notes then touch on massive black hole formation and growth mechanisms, emphasizing the processes at play at early cosmic times. Then techniques for modeling the cosmic massive black hole evolution, are reviewed with an emphasis on cosmological simulations, before approaching how observables are derived from models. They conclude with a section reflecting on the main questions on the JWST-discovered population in light of the material presented in the earlier sections.