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 α in the observationally relevant redshift interval z ≃0-5, within a rather general theoretical framework. We find a worst case upper limit for Δα/α of 8 × 10 −6 for z ≤5 and Δα/α of 0.9 × 10 −6 for z ≤1.6. The derived limits are at variance with the recent findings by Webb et al., who claim an observed variation of Δα/α=-2.6±0.4 × 10 −5 at 1< z <1.6.