Seed and vacuum pair production in strong laser field

Researches on the electron-positron pair production in the presence of the intense laser field are reviewed, motivated by the theoretical importance of the nonperturbative QED problem and the worldwide development of high power laser facilities. According to the distinct experimental requirements and theoretical methods, two types of pair production are elaborated, which are, respectively, pair production in the combination of a seed particle and the strong laser, and vacuum pair production without a seed particle. The origin of the nonperturbative problem caused by the strong field is analyzed. The main ideas, realisation, achievements, validity, challenges and bottleneck problems of the nonperturbative methods developed for each type of the pair production problem are discussed.