Markov Chain Monte Carlo is a method to simulate a desired probability distribution via constructing a Markov chain whose stationary distribution is the distribution we want to simulate. Mixing time describes the rate of convergence of the Markov chain to the stationary distribution. We will give examples of Gibbs sampling algorithms (also known as Glauber dynamics). We will explain how strong stationary time and coupling are used to obtain bounds on mixing time. We will also discuss new approaches to coupling method and their applications.