Schwarz domain decomposition methods are iterative methods for solving systems of equations, which can be defined at the PDE level. It can also be viewed as generalization of the classical block Jacobi and Gauss-Seidel methods by changing overlap and boundary conditions of the blocks (subdomains) and often adding coarse correction steps. Regarding the boundary conditions of subdomains, it turns out useful to think of the subdomain problems as domain truncation of the original problem, and the exact truncation by transparent boundary conditions leads to optimal Schwarz methods that converge in finite steps. It then becomes a key idea to approximate these transparent boundary conditions for fast convergence of Schwarz methods. The goal of this talk is to give an overview of such methods and their analysis.