The rapid growth of urbanization and industrialization has escalated issues of ground-borne and seismic vibrations, posing risks to infrastructure stability, equipment integrity, and environmental quality. Conventional solutions, such as passive barriers and active vibration cancellation systems, often demonstrate limited effectiveness, particularly against low-frequency vibrations from sources like railways, heavy machinery, construction, and seismic activity. This Minisymposium will therefore highlight advanced research of elastic and locally resonant metamaterials engineered to control, redirect, and mitigate both natural and anthropogenic vibrations.