Organic peroxides are widely used to initiate polymerization of olefins, e.g. the formation of polyethylene.  A key step is homolysis:
The tendency to homolyze is also exploited to modify polymers by grafting or visbreaking, or cross-link polymers to create a thermoset. When used for these purposes, the peroxide is highly diluted, so the heat generated by the exothermic decomposition is safely absorbed by the surrounding medium (e.g. polymer compound or emulsion).