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After reviewing some recent progress on the Boltzmann equation without angular cutoff,we will present some recent progress on the measure valued solutions.The celebrated H-Theorem implies that large time behavior of solutions to the Boltzmann equation is given by an equilibrium state given in the form of a Maxwellian distribution.This has been justified in verious settings together with convergence rate when the initial energy is finite.On the other hand,when the initial energy is infinite,other time asymptotic states in the form of self-similar solutions are ob-tained and the convergence is justified for the spatially homogeneous Boltzmann equation with Maxwellian type cross sections for the measure valued solutions.This is a joint work with Yoshinori Morimoto and Huijiang Zhao.