This chapter presents an overview of methods for addressing two practical tasks: monitoring convergence of the simulation and summarizing inference about the target distribution using the output from the simulations. The material in Sections 8.3~8.5 is presented in more detail, with an example, in Gelman and Rubin (19926). Section 8.6 introduces and provides references to various methods in the recent statistical literature for using inference from the simulation to improve the efficiency of the Markov chain algorithm.