These are the proceedings of the 18th international conference on domain decomposition methods in science and engineering, held in Jerusalem, January 12-17, 2008. Domain decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems into account. This is essential for approaching peak floating point performance. There is an increasingly well developed theory which is having a direct impact on the development and improvements of these algorithms.