Does the Fine Structure Constant Really Vary in Time?

We discuss how laboratory experiments can be used to place constraints on possible variations of the fine structure constant alpha in the observationally relevant redshift interval z ~= 0 - 5, within a rather general theoretical framework. We find a worst case upper limit for Delta alpha / alpha of 8 x 10^-6 for z <= 5 and Delta alpha / alpha of 0.9 x 10^-6 for z <= 1.6. The derived limits are at variance with the recent findings by Webb et al. (1998), who claim an observed variation of Delta alpha/alpha = -2.6 +- 0.4 x 10^-5 at 1<z<1.6.