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Dark matter structures within strong gravitational lens galaxies and along their line of sight leave a gravitational imprint on the multiple images of lensed sources. Strong gravitational lensing provides, therefore, a key test of different dark matter models in a way that is independent of the baryonic content of matter structures on subgalactic scales. In this chapter, we describe how galaxy-scale strong gravitational lensing observations are sensitive to the physical nature of dark matter. We provide a historical perspective of the field, and review its current status. We discuss the challenges and advances in terms of data, treatment of systematic errors and theoretical predictions, that will enable one to deliver a stringent and robust test of different dark matter models in the near future. With the advent of the next generation of sky surveys, the number of known strong gravitational lens systems is expected to increase by several orders of magnitude. Coupled with high-resolution follow-up observations, these data will provide a key opportunity to constrain the properties of dark matter with strong gravitational lensing.
Vegetti et al. (Tue,) studied this question.