  We summarize and explain the current status of variations of fundamental
masses in cosmology, with a particular focus on variations of the electron
mass. We show that electron mass variations not only allow for significant
easing of the Hubble tension but are also preferred at a decent level of
significance using the latest DESI data (between $2\sigma$ and $3.6\sigma$
depending on the model and the data). This extreme success of the model is
neither tightly constrained from light element abundances generated during big
bang nucleosynthesis nor from post-recombination observations using quasars and
atomic clocks, though future data is expected to give strong evidence in favor
of or against this model. Models of baryon mass variations, on the other hand,
are shown to generally not be cosmologically interesting.
