After reviewing some recent progress on the Boltzmann equation without angular cutoff, we will present some recent progress on the measure value solutions. The celebrated H- Theorem implies that the 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 setting together with convergence rate when the initial energy is finite. On the other hand, wthen the initial energy is infinite, other time asymptotic states in the form of self-similar solutions are obtained and the convergence is justified for the spatially homogeneous Boltzmann equation with Maxwellian type cross sections for the measure value solutions. This is a joint work with Yoshinori Morimoto and Huijiang Zhao.