This chapter reveals that the domain decomposition method has been widely used for solving time dependent PDEs. It dates back to the classical Schwartz alternating algorithm with overlapping subdomains for solving elliptic boundary value problems. Advantages of using domain decomposition approach include high level of parallelism, efficient treatment of complex geometries, and reduction of computational complexity and storage. When solving time dependent PDEs using non-overlapping subdomains, the domain decomposition method could either be used as a preconditioner for Krylov type algorithms, or as a means to decompose the original domain into subdomains and to solve the PDEs defined in different subdomains concurrently. When it is used as a preconditioner, the relevant PDE is discretized over the entire original domain to form a large system of algebraic equations, which is then solved by Krylov type iterative algorithms.