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The ability to steer and focus light inside scattering media has long been sought for a multitude of applications. At present, the only feasible strategy to form optical foci inside scattering media is to guide photons by using either implanted or virtual^,, guide stars, which can be inconvenient and limits the potential applications. Here we report a scheme for focusing light inside scattering media by employing intrinsic dynamics as guide stars. By adaptively time-reversing the perturbed component of the scattered light, we show that it is possible to focus light to the origin of the perturbation. Using this approach, we demonstrate non-invasive dynamic light focusing onto moving targets and imaging of a time-variant object obscured by highly scattering media. Anticipated applications include imaging and photoablation of angiogenic vessels in tumours, as well as other biomedical uses.