This Minisymposium aims at exploring the theoretical frameworks, relationships and integration strategies between classical local continuum methods and emerging nonlocal computational models, such as peridynamics and phase-field. While nonlocal models have found extensive application in fracture and damage mechanics, understanding their theoretical foundations, performance characteristics, and their possible combination with local models opens new possibilities in computational mechanics. This Minisymposium invites contributions that evaluate, apply, and compare these methods across a wide variety of application areas, including corrosion and material degradation, heat and mass transport in heterogeneous media, biomedical systems (e.g., bioresorbable implants), and evolving microstructures. Particular attention will be placed onto innovative computational and algorithmic approaches that allow for robust connections, integrations, and unification frameworks for local and nonlocal modeling approaches. Contributions involving computational efficiency, scalability in high-performance computing (HPC) environments, and the application of artificial intelligence and machine learning to facilitate or enhance these connections are especially welcome. This Minisymposium intends to stimulate interdisciplinary discussion among researchers from computational mechanics, applied mathematics, materials science, and biomedical engineering, highlighting shared computational challenges and collaborative opportunities.