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The DAMPE experiment recently published its first results on the lepton ($e^++ e^-$) cosmic-ray (CRs) flux. These results are of importance since theyaccount for the first direct detection of the lepton break around the energy of1 TeV and confirm the discoveries of ground-based Cherenkov detectors.Meanwhile they reveal a new high-energy feature in the spectrum which triggereda lot of excitement on the theory side, when interpreted as the typicalsignature of leptophilic dark-matter annihilation. In this proceeding I mainlyfocus on the theoretical understanding of the lepton break. Then I quicklyreview the status of the more speculative line-like DAMPE excess, whoseastrophysical (pulsar) or exotic (dark matter) explanation is stronglyconstrained by multi-messenger astronomy.

Theoretical interpretations of DAMPE first results: a critical review