  The dust abundance of the interstellar medium plays an important role in
galaxy physics, the chemical evolution of matter and the absorption and
re-emission of stellar light. The last years have seen a surge in observational
and theoretical studies constraining the dust-abundance of galaxies up to
$z\sim5$. In this work we gather the latest observational measurements (with a
focus on absorption studies covering metallicities in the range $6.8 < 12 +
\log{(O/H)}<9$) and theoretical predictions (from six different galaxy
formation models) for the dust-to-gas (DTG) and dust-to-metal (DTM) ratio of
galaxies. The observed trend between DTG and DTM and gas-phase metallicity can
be described by a linear relation and shows no evolution from $0<z<5$.
Importantly, the fit to the DTG-metallicity relation provides a refined tool
for robust dust-based gas mass estimates inferred from millimeter
dust-continuum observations. The lack of evolution in the observed relations
are indicative of a quickly reached balance (already when the Universe was 1.2
Gyr old) between the formation and destruction of dust and a constant timescale
for star-formation at fixed metallicities over cosmic time. None of the models
is able to reproduce the observed trends over the entire range in metallicity
and redshift probed. The comparison between models and simulations furthermore
rules out some of the current implementations for the growth and destruction of
dust in galaxy formation models and places tight constraints on the predicted
timescale for star-formation.
