This article reviews recent work on the possible variability of basic physical constants, such as the charge of the electron e, Planck's constanthand the gravitational constantG. The problem was first raised by Dirac as early as 1937. Its present state is here discussed, together with new suggestions which include Gamow's hypothesis that the fine-structure constant varies directly with time (e2/hc ∞ t), the hypothesis (e2∞t, h ∞ t, G ∞ t) and the hypothesis (e4∞t, h2∞t, G=constant).