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Deciphering the nature of dark matter remains one of the major open mysteries of present-day physics. The prime channel thereby are direct detection experiments aiming to observe interactions of dark matter particles in their detectors. This is challenging because dark matter interactions are anticipated to be rare, to deposit only very little energy and to result in a featureless energy spectrum. The latter challenge may be met by exploiting the expected annual modulation of the event rate which is a very powerful tool, in particular in the presence of backgrounds. 

The DAMA/LIBRA experiment observes such an annual modulation signal at high confidence which contradicts null-results of numerous other experiments in the so-called standard scenario. In this talk I will review the current experimental results relevant to this contradiction and give an outlook on ongoing and future experimental efforts to solve it.

A particular focus thereby will be on the COSINUS experiment aiming for a model-independent cross-check of the DAMA signal. Such a cross-check is absent up to now and necessarily requires the use of the same target material (NaI). In addition, COSINUS has the potential to give new insight on the potential interaction mechanism by operating NaI as cryogenic detector providing particle discrimination on an event-by-event basis - a unique feature for NaI-based dark matter searches. 

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