Development of superintense laser technology has brought historic opportunities and space to expand for the study of interaction between light and matter. The process of nuclear reaction assisted by superintense laser field, especially the influence on cross sections of deuteron-triton fusion reaction, has attracted more and more attention. In this paper, we introduce the rapid development of laser technology and the wide application of superintense laser technology. Then we introduce the cross sections of nuclear fusion reaction and its influencing factors, and review recent progress in the study of light nuclear fusion cross sections in superintense laser field with emphasis on deuteron-triton fusion reaction. At last, we make some prospects for future development in this direction.