Certificateless public key cryptography (CL-PKC for short) is a new type of public key cryptography, which is developed on the foundation of identity based cryptography (ID-PKC for short). CL-PKC elimilates the key escrow problem and the need for public key certificate. These two advantages are what makes it attractive to the research community and industrial world form the beginning of its birth. It has been a very active research hot topic in the field of cryptology and information security. In about seven years, the study of CL-PKC has advanced step by step, making its theories and techniques more and more enriching. This paper revisits, analyzes, compares, and briefly reviews some of the main results. Furthermore, this study discusses some existing problems in this research field that deserve further investigation.