This chapter describes the brief history of iron or cobalt catalysts for olefin polymerisation and oligomerisation. Since the discovery in 1998 that 2,6-bis(imino)pyridine iron and cobalt halides, on activation with MAO, can convert ethylene to highly linear polyethylene, numerous reports have been concerned with ligand modification, mechanisms for precatalyst activation, identifying the active species and understanding the mode of propagation/chain transfer. In addition, heterogenisation of this class of catalysts, their incorporation into macrocycles/ polymers and their use in reactor blending/tandem catalysis has seen some important developments; alternative ligand architectures that can support active iron and cobalt catalysts are also discussed as are different types of olefinic monomer.