  We review the observational information on the constancy of the fine
structure constant alpha. We find that small improvements on the measurement of
^{187}Re lifetime can provide significant progress in exploring the range of
variability suggested by QSO data. We also discuss the effects of a time
varying alpha on stellar structure and evolution. We find that radioactive
dating of ancient stars can offer a new observational window.

Astrophysics;High Energy Physics - Phenomenology;Nuclear Theory