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Semi-active damping control of oscillating devices and structures is a challenging field that conjugates a relative actuators simplicity together with the chance of studying new algorithms and system architectures. This paper proposes an overview of the investigation recently developed by the authors in the field of semi-active damping using the variational optimal control. The method produces a general class of controllers that can be applied to linear as well as nonlinear suspension systems and vibrating structures. Their performances are systematically investigated and compared with the sky-hook benchmark.