Catalytic insertion or addition of a metal-imido/nitrene species, generated from reaction of a transition-metal catalyst with iminoiodanes, to C-H and C=C bonds offers a convenient and atom economical method for the synthesis of nitrogen-containing compounds. Following this groundbreaking discovery during the second half of the last century, the field has received an immense amount of attention with a myriad of impressive metal-mediated methods for the synthesis of amines and aziridines having been developed. This review will cover the significant progress made in improving the efficiency, versatility and stereocontrol of this important reaction. This will include the various iminoiodanes, their in situ formation, and metal catalysts that could be employed and new ligands, both chiral and non-chiral, which have been designed, as well as the application of this functional group transformation to natural product synthesis and the preparation of bioactive compounds of current therapeutic interest.