Theoretical interpretations of DAMPE first results: a critical review

The DAMPE experiment recently published its first results on the lepton ($e^+ + e^-$) cosmic-ray (CRs) flux. These results are of importance since they account for the first direct detection of the lepton break around the energy of 1 TeV and confirm the discoveries of ground-based Cherenkov detectors. Meanwhile they reveal a new high-energy feature in the spectrum which triggered a lot of excitement on the theory side, when interpreted as the typical signature of leptophilic dark-matter annihilation. In this proceeding I mainly focus on the theoretical understanding of the lepton break. Then I quickly review the status of the more speculative line-like DAMPE excess, whose astrophysical (pulsar) or exotic (dark matter) explanation is strongly constrained by multi-messenger astronomy.