The multiblock method traces back to the idea of domain decomposition proposed by the German mathematician Schwarz in 1869. Now, domain decomposition has evolved into a powerful, indispensable approach for numerically solving partial differential equations of fluid flows. This chapter presents the domain decomposition method in a relatively straightforward manner, making it understandable without advanced mathematical knowledge. The chapter starts with the classic Schwarz method for a boundary value problem of the Laplace equation. It introduces basic concepts, including subdomains, interfaces, and interface/transmission conditions, followed by a discussion on the convergence of the method. Then, this chapter proceeds to the computation of a time-dependent problem, and it presents the frameworks of two methods to be followed in the subsequent chapters: the conventional Schwarz method and the Schwarz waveform relaxation method. Furthermore, the discussion proceeds to domain decomposition at the discrete level, now a foundation for parallel computation. It presents relevant techniques, such as the multiplicative Schwarz method, the additive Schwarz method, and the Schur complement system.