Facing severe challenges from climate change, environment and energy in the 21^st century, power systems have been udergoing certain new developing trends.The developing trends of power systems are discussed and summarized in this paper as follows: more incorporation of renewable energy, more adoption of distributed power systems based on micro-grids, more DC type of transmission and distribution, and becoming more electronic.Then the challenges to power electonics, which is the core technology for electric power conversion and control, under such developing trends are analyzed.Some of these challenges can be solved by the research and development efforts within power electronics area, while the others can only be addressed and coped with through close collaboration between power electronics and the related areas.