  I review recent constraints on and claimed detections of a time-varying
fine-structure constant $\alpha$, and discuss our own work, particularly on the
effects of $\alpha$ in the cosmic microwave background and large-scale
structure. Our results are consistent with no variation in $\alpha$ from the
epoch of recombination to the present day, and restrict any such variation to
be less than about 4%. The forthcoming MAP and Planck experiments will be able
to break most of the currently existing degeneracies between $\alpha$ and other
parameters, and measure $\alpha$ to better than percent accuracy.
