I will first review the known results on (mass) concentration phenomenon for solutions to NLS with finite time of existence (blow up solutions), and then will focus on cubic NLS in 2D, in particularly, establish the dependence between the window size of concentration and the rate of explosion of the space-time (Strichartz) norm by revisiting Bourgain's argument (98) in one direction and using the frequency restriction in the opposite. Finally, I will discuss L3 norm concentration for cubic NLS in 3D (joint work with J. Colliander and J. Holmer).