Pressure as a very important dimension independent of temperature and chemical compositions, can effectively change the inter-atomic interaction, induce the formation of high pressure structures with new physical properties, reveal new phenomena and physical rules, and fabricate new materials that can not be synthesized under ambient pressure. At ambient conditions, elements usually adopt simple structures; however, application of pressure induces complex phase transitions with the formation of intriguing high pressure phases, some of which possess novel superconductivity and superhard properties, and even experience metal-insulator transitions. These high pressure phase transitions have attracted worldwide attention. This article reviews the structural transitions of the first 12 light elements in the periodical table under pressure, and discusses novel properties of the new high pressure phases and the corresponding phase transition mechanisms. The prospects of the future experimental and theoretical methods for investigation of high pressure phase transitions are presented.