In this talk, we will first present a general framework for analyzing the spectrum structure of kinetic equations and apply it to the Boltzmann equation without angular cutoff and the Landau equation. And then we will present some results on the spectrum analysis for the Vlasov-Poisson-Boltzmann system and the Vlasov-Maxwell-Boltzmann system. Some applications of these results on spectrum structures will also be given. These are some joint works with Hongjun Yu, Hailiang Li and Mingying Zhong.