The history and development about the study of positrons generated by intense laser interaction with the plasmas are introduced. The mechanisms of the positron generation are presented. Specially, the typical experiment scheme (direct and indirect) of the positron generation, including important results about the experiment and computer simulation are described systemically. Eventually, the study of positron is reviewed and summarized. At present, the conclusions obtained from theoretical research and experimental research are quite different, and a lot of detailed work needs to be done in terms of laser equipment, experimental scheme design, and theoretical and simulation research.