Progress in the development of transition metal catalysts for the polymerization of ethylene and α-olefins is reviewed and analyzed. Further developments involving the use of supported catalysts are detailed and some of the fundamental catalayst—forming reactions are discussed. So, recent kinetic and active centre concentration determinations on the polymerization of 4—methylpentene —1 by catalysts of the type σ—TiCl3.0.33A1C13—Al(i—Bu)3 and supported catatysts of the type MgCl2 / EB / TiCl4-Al(i—Bu)3 are reported and the results analyzed. The much higher activities obtained with MgCl2—supported catalysts are shown to arise from a significant increase in the concentration of active centres together with some increase in the propagation rate constant.