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Crystal scintillators and in particular inorganic scintillators play an important role in the investigation of Dark Matter (DM) and other rare processes. The investigation of a DM signature, as the annual modulation, or the directionality technique requires the use of highly radiopure detectors able to explore the very low energy region maintaining a high stability of the running conditions. In this paper, the cases of NaI(Tl), ZnWO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>4</mn></msub></semantics></math></inline-formula> and SrI<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>(Eu) crystal scintillators are described in the framework of our activities at the Gran Sasso National Laboratory of the INFN. Their role, the obtained results in DM investigation, as well as their potential and perspectives for the future are reviewed.