Cosmic-ray antiprotons are a powerful tool for astroparticle physics. While the bulkof measured antiprotons is consistent with a secondary origin, the precise data of theAMS-02 experiment provides us with encouraging prospects to search for a subdominantprimary component,e.g.from dark matter. In this brief review, we discuss recent limitson heavy dark matter as well as a tentative signal from annihilation of dark matter witha mass.100 GeV. We emphasize the special role of systematic errors that can affect thesignal. In particular, we discuss recent progress in the modeling of secondary productioncross sections and correlated errors in the AMS-02 data, the dominant ones originatingfrom uncertainties in the cross sections for cosmic-ray absor...