With the rapid development of laser technology and the continuous improvement of laser intensity, the process of electron-positron pair creation in vacuum under super strong external field, namely the process of energy conversion to mass, has become a research hot spot. In this paper, we mainly review the progress of quantum Vlasov equation and computational quantum field theory (numerical solution of Dirac equation) in the study of the electron-positron pair production in vacuum under intense laser field in recent years, and introduce two situations of particle pair generation spatially homogeneous field and spatially inhomogeneous field, separally. In the first case, there are electron-positron pair production in oscillating electric fields with double-pulse structure, electron-positron pair generation in the strong dual frequency oscillating electric field, electron-positron pair production in frequency modulated laser fields, and resolving rapidly chirped external fields with Dirac vacuum are introduced. The second case mainly introduces the optimization of spatially localized electric fields for electron-positron pair creation, enhanced pair creation by an oscillating potential with multiple well-barrier structures in space, electron-positron pair production in an oscillating Sauter potential, manipulation of the vacuum to control its field-induced decay and Dirac vacuum as a transport medium for information and transition between coherent and incoherent chirping mechanisms in electron-positron pair production.