In this presentation, I will review the history and literature debate about the anomalous gamma-ray emission detected towards the inner Galaxy by the Fermi-LAT telescope.
The so-called Fermi GeV excess has been first discovered in the early 2010s and later characterised by several, independent, research groups.
While its main features are well established, the details of its spectral energy distribution and morphology remain debated.
Also the nature of this anomalous signal is unknown. Different interpretations have been put forward and scrutinised.
I will provide an overview of the most promising interpretations in terms of dark matter emission and faint astrophysical sources, and offer an outlook on how we can try to disentangle these two hypotheses with multi-wavelength and multi-messenger astrophysics.