With detections of quasars powered by increasingly massive black holes at increasingly early times in cosmic history over the past decade, there has been correspondingly rapid progress made on the theory of early black hole formation and growth. Here, we review the emerging picture of how the first massive black holes formed from the primordial gas and then grew to supermassive scales. We discuss the initial conditions for the formation of the progenitors of these seed black holes, the factors dictating the initial masses with which they form, and their initial stages of growth via accretion, which may occur at super-Eddington rates. Finally, we briefly discuss how these results connect to large-scale simulations of the growth of supermassive black holes in the first billion years after the Big Bang.

Since the beginning of the new millennium, more than 100 z ~ 6 quasars have been discovered through several surveys and followed-up with multi-wavelength observations. These data provided a large amounts of information on the growth of supermassive black holes at the early epochs, the properties of quasar host galaxies and the joint formation and evolution of these massive systems. We review the properties of the highest z quasars known so far, especially focussing on some of the most recent results obtained in (sub-)millimetre bands. We discuss key observational challenges and open issues in theoretical models and highlight possible new strategies to improve our understanding of the galaxy black hole formation and evolution in the early Universe.

The formation, assembly history, and environmental impact of the massive black holes (BH) that are ubiquitous in the nuclei of luminous galaxies today remain some of the main unsolved problems in cosmic structure formation. In the last several years, it has become clear that quasars are not just tracers of early and recent structure formation, but that they seem to have actively influenced galaxies and clusters through feedback mechanisms that are still not well understood. The discovery of more and more numerous quasars at redshift above 6, powered by BHs with masses similar to that of their local counterparts, further complicates this scenario. This emphasises the urgent need to better understand how and when such massive objects form and grow, what is the strength and scale of their impact on the evolution of their host galaxies, and what are the main physical processes driving and regulating this co-evolution.

The detection of quasars at z > 6 unveils the presence of supermassive black holes of a few billion solar masses. The rapid formation process of these extreme objects remains a fascinating and open issue. Such discovery implies that seed black holes must have formed early on, and grown via either rapid accretion or BH/galaxy mergers. In this theoretical review, we discuss in detail various BH seed formation mechanisms and the physical processes at play during their assembly. We discuss the three most popular BH formation scenarios, involving the (i) core-collapse of massive stars, (ii) dynamical evolution of dense nuclear star clusters, (iii) collapse of a protogalactic metal free gas cloud. This article aims at giving a broad introduction and an overview of the most advanced research in the field.

Observational constraints on the birth and early evolution of massive black holes come from two extreme regimes. At high redshift, quasars signal the rapid growth of billion-solar-mass black holes and indicate that these objects began remarkably heavy and/or accreted mass at rates above the Eddington limit. At low redshift, the smallest nuclear black holes known are found in dwarf galaxies and provide the most concrete limits on the mass of black hole seeds. Here, we review current observational work in these fields that together are critical for our understanding of the origin of massive black holes in the Universe.