  The detection of quasars at $z>6$ unveils the presence of supermassive black
holes (BHs) 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.
