The focus of this dissertation is on incorporating rate-independent linear damping (RILD) in low-frequency dynamic systems such as base-isolated structures, inter-story isolated buildings, and vehicle suspension systems. RILD is a promising damping model for low-frequency structures because it provides direct control over displacement. Because the control force generated by RILD is proportional to displacement (advanced in phase by π/2 radians) and independent of frequency, it performs well under both low-frequency and high-frequency excitations (relative to the structure’s fundamental natural frequency). The π/2 radians phase advance makes RILD non-causal, which has hindered its practical applications. This dissertation proposes causal semi-active controllers and passive mechanical systems to approximate RILD in different areas of vibration control engineering. Numerical simulations, shake table tests, and real-time hybrid simulation (RTHS) tests are conducted to demonstrate the performance of the proposed causal approaches. The results compare well to non-causal simulations in both the achieved forces and system responses. Through the proposed algorithms and devices, RILD is shown to be an attractive and practical damping alternative for the vibration mitigation of low-frequency structures.