  In this paper I review some old and new works on the computation of two-loop
4-particle amplitude in superstring theory. I also present the proof by Iengo,
showing the vanishing of the term related to the two-loop correction to the
$R^4$ term. Finally I will present some recent works on two-loop computation in
hyperelliptic language following the new gauging fixing method of D'Hoker and
Phong.
