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Much experimental work has been done on the dielectric breakdown of solid dielectrics, and a number of breakdown theories have been proposed. Many problems, however, still remain on the breakdown process of polymers. Here, the breakdown process of polymers are discussed from the standpoint of the inherent properties of polymers such as chemical structure, structural irregularities, the presence of additives, molecular motion, and so on. Further, as for the long-time breakdown processes of polymer insulation systems, electrical degradations caused by (PD) and treeing breakdown have been mentioned as important factors. Using experimental results obtained in our laboratory together with those presented by others, our considerations for fundamental processes of electrical degradation are reported. Also, the behavior of dc trees caused by space charge accumulation are discussed with the nature of carrier injection and trapping in polymers, which are estimated by TSC and TL measurements.