The rapid growth of hardware parallelism, particularly through GPUs, has opened new opportunities for solving large-scale linear systems. Yet, exploiting the full performance of modern architectures remains challenging, as communication bottlenecks limit the scalability of classical iterative solvers at extreme scales. Classically, domain decomposition (DD) and multigrid (MG) have been among the most efficient iterative strategies: DD partitions problems into localized subproblems suited for parallelism, while MG accelerates convergence through hierarchical error reduction. Both, however, face limitations at scale - DD through frequent interface exchanges and potential load imbalance, MG through difficulties with complex geometries, irregular discretizations, or anisotropy, and its more dense communication pattern, where the most successful multiplicative approach involves neighbor-communication for residuals on every level and the for level transfer, eventually embedding a reduction-broadcast type structure interleaved with computations. We explore DD and MG methods in the context of exascale computing, focusing on GPU-optimized MG solvers and on developing a more general framework that integrates these complementary strategies. By investigating MG techniques not only as solvers for global problems but also in the context of interface equations within DD, we explore pathways to alleviate scaling bottlenecks. We aim to contribute to robust, architecture-aware solvers that combine the strengths of DD and MG, with the long-term goal of enabling more scalable iterative methods for next-generation scientific and engineering applications.