Where do the AMS-02 antihelium events come from?

We discuss the origin of the antihelium-3 and -4 events possibly detected by AMS-02. Using up-to-date semianalytical tools, we show that spallation from primary hydrogen and helium nuclei onto the ISM predicts a (He-3) over bar flux typically one to two orders of magnitude below the sensitivity of AMS-02 after 5 years, and a (He-4) over bar flux roughly 5 orders of magnitude below the AMS-02 sensitivity. We argue that dark matter annihilations face similar difficulties in explaining this event. We then entertain the possibility that these events originate from antimatter-dominated regions in the form of anticlouds or antistars. In the case of anticlouds, we show how the isotopic ratio of antihelium nuclei might suggest that BBN has happened in an inhomogeneous manner, resulting in antiregions with a antibaryon-to-photon ratio (eta) over bar similar or equal to 10(-3) eta. We discuss properties of these regions, as well as relevant constraints on the presence of anticlouds in our Galaxy. We present constraints from the survival of anticlouds in the Milky-Way and in the early Universe, as well as from CMB, gamma-ray and cosmic-ray observations. In particular, these require the anticlouds to be almost free of normal matter. We also discuss an alternative where antidomains are dominated by surviving antistars. We suggest that part of the unidentified sources in the 3FGL catalog can originate from anticlouds or antistars. AMS-02 and GAPS data could further probe this scenario.