The rapid growth of hardware parallelism, particularly with the rise of GPUs, has opened new avenues for efficiently solving large-scale linear systems. However, the optimal use of performance capabilities of modern architectures remains challenging due to communication bottlenecks that limit the scalability of classical iterative solvers at extreme scales. Among the most effective strategies to address these challenges are domain decomposition and multigrid methods, each with a long history of development. Domain decomposition techniques partition global problems into localized subproblems that can be solved separately, enabling high parallelism and reducing global communication. Multigrid methods — including geometric, algebraic, and polynomial variants — accelerate convergence by addressing errors across multiple scales through hierarchies of discretizations, often achieving optimal or near-optimal computational complexity. However, each concept faces potentially severe limitations: domain decomposition may suffer from slow convergence due to frequent interface data exchange and load imbalance, while multigrid methods can struggle with complex geometries, irregular meshes, or highly anisotropic coefficients. In recent years, systematic efforts to combine these two classes of methods — such as using multigrid as a preconditioner within domain decomposition frameworks, applying domain decomposition smoothers in multigrid hierarchies, or developing hybrid solvers tailored to large-scale, heterogeneous systems — have gained increasing attention. Advances in both domain decomposition and multigrid techniques, whether developed independently or in combination, offer powerful and complementary tools for building robust and scalable solvers for complex physical problems encountered in science and engineering. This minisymposium aims to bring together various strains of developments for scalable solvers, inviting novel research on both domain decomposition and multigrid methods as well as their combination. Topics include, but are not limited to, heterogeneous coupling strategies for coupled, multiphysics, and multiscale problems; communication avoiding techniques; and approaches for optimizing performance on modern computing architectures.