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Transitions in atoms and molecules provide an ideal test ground forconstraining or detecting a possible variation of the fundamental constants ofnature. In this Perspective, we review molecular species that are of specificinterest in the search for a drifting proton-to-electron mass ratio $\mu$. Inparticular, we outline the procedures that are used to calculate thesensitivity coefficients for transitions in these molecules and discuss currentsearches. These methods have led to a rate of change in $\mu$ bounded to $6\times 10^{-14}$/yr from a laboratory experiment performed in the presentepoch. On a cosmological time scale the variation is limited to$|\Delta\mu/\mu| < 10^{-5}$ for look-back times of 10-12 billion years and to$|\Delta\mu/\mu| < 10^{-7}$ for look-back times of 7 billion years. The lastresult, obtained from high-redshift observation of methanol, translates into$\dot{\mu}/\mu = (1.4 \pm 1.4) \times 10^{-17}$/yr if a linear rate of changeis assumed.

Perspective: Tipping the scales - search for drifting constants from molecular spectra