A nuclear clock has the potential to be particularly sensitive to possible time variations of the fine-structure constant. The central idea is that a nuclear transition couples differently to the fine-structure constant than an atomic shell transition does. For this reason a comparison of the frequency of a nuclear clock with an atomic clock could lead to an extraordinary high sensitivity for potential time variations of the fine structure constant. The achievable factor of sensitivity, however, remains subject to speculation. Recent measurements and analysis are consistent with enhancement factors on the order of 10.