Do the fundamental constants change with time ?

Comparisons between the redshifts of spectral lines from cosmologically-distant galaxies can be used to probe temporal changes in low-energy fundamental constants like the fine structure constant and the proton-electron mass ratio. In this article, I review the results from, and the advantages and disadvantages of, the best techniques using this approach, before focussing on a new method, based on conjugate satellite OH lines, that appears to be less affected by systematic effects and hence holds much promise for the future.