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Radioactive nuclei are the key to understanding the circumstances of the birth of our Sun because meteoritic analysis has proven that many of them were present at that time. Their origin, however, has been so far elusive. The ERC-CoG-2016 RADIOSTAR project is dedicated to investigating the production of radioactive nuclei by nuclear reactions inside stars, their evolution in the Milky Way Galaxy, and their presence in molecular clouds. So far, we have discovered that: (i) radioactive nuclei produced by slow (107Pd and 182Hf) and rapid (129I and 247Cm) neutron captures originated from stellar sources —asymptotic giant branch (AGB) stars and compact binary mergers, respectively—within the galactic environment that predated the formation of the molecular cloud where the Sun was born; (ii) the time that elapsed from the birth of the cloud to the birth of the Sun was of the order of 107 years, and (iii) the abundances of the very short-lived nuclei 26Al, 36Cl, and 41Ca can be explained by massive star winds in single or binary systems, if these winds directly polluted the early Solar System. Our current and future work, as required to finalise the picture of the origin of radioactive nuclei in the Solar System, involves studying the possible origin of radioactive nuclei in the early Solar System from core-collapse supernovae, investigating the production of 107Pd in massive star winds, modelling the transport and mixing of radioactive nuclei in the galactic and molecular cloud medium, and calculating the galactic chemical evolution of 53Mn and 60Fe and of the p-process isotopes 92Nb and 146Sm.