The rigorous justification of mean-field type equations (Boltzmann,
Vlasov-Poisson, NLS...) from the many-body systems they are supposed to
describe is a vast and fundamental subject. In this talk, we talk about
recent advances in this area on the derivation of focusing nonlinear
Schrodinger equations (NLS) from quantum many-body evolutions in the
context of Bose-Einstein condensation, which has been one of the most
active areas of contemporary research since the Nobel prize winning
experiments. We survey the background and the evolution of the results
and techniques in the field during the talk.