The importance of cis-trans isomerism of alkenes in polymer chemistry can be shown by the chemistry of isoprene, or 2-methyl-1,3-butadiene. If natural rubber is heated strongly it smells of isoprene - which led early polymer chemists to believe that this was a building block or monomer.
Early polymerisation experiments with isoprene were not succesful. In nature the rubber tree links the isoprene units cis- to each other, while the early experiments had a mixture of cis- and trans- links, which provided a sticky mess.

The sap obtained from the rubber tree, if heated, forms an all trans- orientated link natural polymer known as gutta-percha. This is quite a hard material and a common use is the covering of golf balls:

The polymer chains lie in tight coils, and by stretching the rubber the coils are untangled.