  Galaxy groups host the majority of matter and more than half of all the
galaxies in the Universe. Their hot ($10^7$ K), X-ray emitting intra-group
medium (IGrM) reveals emission lines typical of many elements synthesized by
stars and supernovae. Because their gravitational potentials are shallower than
those of rich galaxy clusters, groups are ideal targets for studying, through
X-ray observations, feedback effects, which leave important marks on their gas
and metal contents. Here, we review the history and present status of the
chemical abundances in the IGrM probed by X-ray spectroscopy. We discuss the
limitations of our current knowledge, in particular due to uncertainties in the
modeling of the Fe-L shell by plasma codes, and coverage of the volume beyond
the central region. We further summarize the constraints on the abundance
pattern at the group mass scale and the insight it provides to the history of
chemical enrichment. Parallel to the observational efforts, we review the
progress made by both cosmological hydrodynamical simulations and controlled
high-resolution 3D simulations to reproduce the radial distribution of metals
in the IGrM, the dependence on system mass from group to cluster scales, and
the role of AGN and SN feedback in producing the observed phenomenology.
Finally, we highlight future prospects in this field, where progress will be
driven both by a much richer sample of X-ray emitting groups identified with
eROSITA, and by a revolution in the study of X-ray spectra expected from
micro-calorimeters onboard XRISM and ATHENA.
