Anti- and hyper-nuclei at the LHC and in the cosmos

The ALICE collaboration has recently released a series of measurements of the production of anti and hyper-nuclei in pp, p-Pb, and Pb-Pb collisions at LHC energies. These results do not only serve to understand the properties of the hot QCD medium created in these collisions, but also help to clarify the origin of the anti-nuclei candidates which are observed by space-borne experiments such as AMS-02. An overview of the existing ALICE results and their interpretation in terms of coalescence and thermal-statistical models will be given. In addition, the talk will focus in particular on the ALICE physics program in the years 2020-2028 which will allow to study these objects with unprecedented precision.