The difficulties encountered in the preparation of polymers that are uniform chemically, structurally, and in their molecular weight are due mainly to the wide variety of possible polymers. This arcticle gives a review of attempts to synthesize homogeneous polymers by chain reactions and by stepwise synthesis. Syntheses on templates are extremely important in living cells; methods have recently been found for syntheses of this type that are independent of natural processes. Uniform polymers can also be obtained by reactions on existing polymers. In replicating polymers, this in principle requires the modification of only one polymer molecule.