I will present some general results on the finite-time blow-up of the mass critical gKdV equation. Then, we will focus on results concerning finite-time infinite-point blow-up. Previously, the blow-up rate of such solutions was limited with a lower bound of 11/13; in my work, this has been improved to 1/2. The critical blow up rate 1/2, is in the transition between infinite and finite point blow up. This year I’ve constructed solutions in the related regime, which is close to my previous work and presents some form of stability. Recently, in the work of Y.Martel and D. Pilod, the interval of finite point blow up rates was also improved, we will introduce these results.