The activity and stability of homogeneous olefin polymerisation catalysts, when immobilised on a support, are dependent on both chemical and physical effects. Chemical factors affecting catalyst activity include the ease of formation of the active species, which is strongly dependent on the transition metal. Catalyst productivity is dependent on the balance between activity and stability. Immobilisation can lead to a lower proportion of active species and therefore lower initial polymerisation activity, but nevertheless give higher polymer yields in cases where increased catalyst stability is obtained. Important physical factors are support porosity and the ability of a support to undergo progressive fragmentation during polymerisation, facilitating monomer diffusion through the growing catalyst/polymer particle. This article illustrates the importance of these factors in olefin polymerisation with both early- and late-transition metal catalysts, with particular reference to the use of silica and magnesium chloride supports as well as to effects of immobilisation on polymer structure and properties.