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Research and development results of enhancement techniques of electrical insulation performance for higher electric field application in power transmission/substation equipment, such as transformers, switchgears and cables, are described, especially based on the view point of dielectric materials. Firstly, the electric field analysis, field optimization and field measurement techniques are introduced to discuss higher electric field stress applications in power equipment. Secondly, material types, including gases, liquids, solids, vacuum and their composite systems are discussed to make power equipment with higher insulation performance, lower losses, lower environmental impact and higher reliability. In the process of development, a highly sophisticated new approach to clarify the physical mechanisms of partial discharges was developed and applied. By the introduction and applications of the above mentioned new electrical insulation techniques based on dielectric materials, concepts of future power equipment with higher electric field stress are proposed. This paper is based on the Whitehead Memorial Lecture given at the IEEE Conference on Electrical Insulation and Dielectric Phenomena (CEIDP) 2011 in Cancun, Mexico.