The direct addition of ammonia or primary and secondary amines to non-activated alkenes and alkynes is potentially the most efficient approach towards the synthesis of higher substituted nitrogen-containing products. It represents the most atom economic process for the formation of amines, enamines and imines, which are important bulk and fine chemicals or building blocks in organic synthesis. While the hydroamination of alkenes is still limited to more or less activated alkenes, great progress has been achieved in the case of alkynes over the last three years. To illustrate this progress, the review will mostly focus on recent developments in the field of intermolecular hydroamination of alkynes. However, if it is necessary for the discussion, older results and intramolecular reactions, which can be achieved more easily, will be mentioned as well.