Complex wavelet transform（CWT） has many advantages that ordinary real wavelet can't provide. Except for providing simple information about amplitude spectrum and phase spectrum， CWT can provide various combined information. The defects of real wavelets are overcome by CWT， such as shift sensitivity， poor directionality and absence phase information. Phase is important characteristic of power system signals. CWT can extract phase information of power system signals. In this paper， various CWT and their performance in recent years are summarized and compared including their applications in power system. In the end， the prospect of CWT is proposed.