Iterative solvers based on domain decomposition originated as means of extending the generality of direct solvers limited by structure or available memory by "divide-and-conquer" and evolved rapidly in the last two decades to general purpose algebraic techniques suited for scalable computer architectures. In this talk, we briefly survey some themes in domain decomposed iterative methods for linear problems: algorithms of Schwarz and Schur types, convergence results, and scalability estimates. We argue the advantages of domain decomposition over other types of parallel algorithms for PDEs on massively parallel machines. We illustrate with recent Gordon Bell prizes based on domain decomposition and mention available software. Finally, we look at some current research interests. One goal of the presentation is to point graduate students to research opportunities at the frontier of parallel solvers for PDE systems, and another is to equip the audience to knowledgeably participate in the 16th international conference on domain decomposition methods to be held in NYC in January (see www.ddm.org).