  We review the recent progress on the long-time behavior for a general class
of focusing $L^2$-critical nonlinear Schr\"odinger equations (NLS) with lower
order perturbations. Two canonical models are the stochastic NLS driven by
linear multiplicative noise and the classical deterministic NLS. We show the
construction and uniqueness of the corresponding blow-up solutions and
solitons, including the multi-bubble Bourgain-Wang type blow-up solutions and
non-pure multi-solitons, which provide new examples for the mass quantization
conjecture and the soliton resolution conjecture. The refined uniqueness of
pure multi-bubble blow-ups and pure multi-solitons to NLS under very low
asymptotical rate is also reviewed. Finally, as a new result, we prove the
qualitative properties of stochastic blow-up solutions, including the
concentration of mass, universality of critical mass blow-up profiles, as well
as the vanishing of the virial at the blow-up time.
