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Nuclear reactions are the driver of the evolution of many astrophysical objects. In the astrophysical environment their respective reaction rates are, however, modified due to the presence of other charges. The effects depend on the relative importance of Coulomb energy versus thermal energy and are distinguished between weak and strong screening. In the extreme case of pycnonuclear reactions, fusion reactions can be induced by the zero-point motion of nuclei in a Coulomb crystal. This paper reviews the various screening situations and discusses important applications. We also briefly review laboratory approaches to study screening effects.