The hydroamination of alkenes, dienes, allenes, and alkynes by early transition metal catalysts has seen significant progress over the last decade, especially with respect to control of regio- and stereoselectivity and the synthesis of more complex nitrogen-containing skeletons. This article provides an overview over the application of catalyst systems based on the 17 rare earth elements, as well as group 4 and group 5 metals. These electropositive metal catalysts operate via activation of the amine to form catalytic active metal-amido or metal-imido species, although the true nature of this species is not known with certainty for all systems and may vary for different substrate classes. This mode of activation differentiates early transition metal catalysts from many late transition metal catalysts that operate via activation of the unsaturated C-C linkage (alkene, 1,3-diene, allene, or alkyne). Alkali metals, alkaline earth metals and aluminum are included in this overview as well, as they show strong similarities in their reactivity and mechanistic pathways to aforementioned early transition metals. While the structure-reactivity principles are well understood for certain hydroamination processes, e.g., in the intramolecular hydroamination of aminoalkenes or the intermolecular hydroamination of alkynes, other transformations, in particular the intermolecular hydroamination of alkenes, remain highly challenging. Due to the potential of the hydroamination process for the synthesis of pharmaceuticals and other industrially relevant fine chemicals, a strong emphasis is given on the application of chiral catalysts in stereoselective processes.