A review with 86 references covering chain-growth (insertion, metathesis) polymerization and step-growth (metathesis polycondensation of acyclic dienes, Heck-type polycondensation of haloarene derivatives, etc.) polymerization, promoted by catalysts based on late transition metals and each dicsussed in relation to monomer and catalyst type. The nature of catalyst's active sites is described and polymerization mechanisms are discussed. The most representative Pd-based catalysts are duly emphasized. The chain -and the step-growth models of propagation of polymerization are intercompared in terms of the oxidation state of the Pd species in the catalysts. The former mode keeps the oxidation state of palladium [Pd(II)] unaffected; the latter mode allows the oxidation state to vary from Pd(II) to Pd(0) (and back).