  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 the strong
laser facilities. According to distinct experimental requirements and
theoretical methods, two types of pair production are elaborated, which are
respectively the 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, realization, achievements, validity, challenges and bottleneck problems
of the nonperturbative methods developed for each type of the pair production
problem are discussed.
