Departing from the weak solution,we prove the uniqueness,smoothing estimates and the global dynamics for the non cutoff spatially homogeneous Boltzmann equation with moderate soft potentials. More precisely, we show that the behavior of the solution(including the regularity and the longtime behavior) can be characterized quantitatively by the initial data at the large velocities, i.e., (i). initially polynomial decay at the large velocities in L1 space will induce the finite smoothing estimates in weighted Sobolev spaces and the polynomial rate(including the lower and upper bounds) of the convergence to the equilibrium; (ii). initially the exponential decay at the large velocities in L1 space will induce C∞regularization effect and the stretched exponential convergent rate. The new ingredients of the proof lie in the development of the localized techniques in phase and frequency spaces and the propagation of the exponential momentum. This is a joint work with Jie Ji.