Radioactive nuclei with half lives of the order of 1 to 100 million years (Myr) can be detected in space by their gamma-ray lines or directly in cosmic rays, and in solar system material probes as sediments and fossils on Earth, and in Moon samples. They indicate - on a cosmic time-scale - that recent nucleosynthesis has been ongoing, and they trace its candidate sources, i.e., massive stars, supernovae, neutron star mergers, etc. Detection in space tells us about the current state of the Galaxy and its recent history of few Myr, whereas detection on Earth tells us about recent supernovae close to Earth. The presence of today extinct radioactivities can be inferred from the analysis of primitive meteoritic inclusions and presolar grains, the former telling us about the formation history of the Solar System, the latter about chemical evolution of the Galaxy, and nucleosynthesis mostly in low-mass stars and supernovae. Key examples of such nuclei include 26 Al, 60 Fe, and 244 Pu. Our goal is to exploit these nuclei and the information that they carry by combining the most current sophisticated experimental, observational, theoretical, and numerical modelling investigations. We will undertake a unique and complete effort to understand the production of these radionuclei in stars and supernovae, their distribution and history in the Galaxy, and how they ended up in the Solar System. Our team includes experts on gamma-ray observations, accelerator mass spectrometry, nuclear experiment and theory, and modelling of stars, supernovae, and galactic chemical evolution. We will take advantage of new nuclear research facilities in China (e.g., JUNA), Europe (FAIR) and USA (FRIB) to obtain nuclear data and we will identify uncertainties in key reaction channels that need to be constrained by future experiments, helping to define the future research program. This becomes particularly powerful in combination with data from current and future international and Chinese gamma-ray observatories through which theory and models can be tested. Our key target is to exploit radioactive nuclei to constrain stellar evolution and nucleosynthesis, the production and propagation of such nuclei, and the timescales of Galactic history and of the origin and history of the matter in our Solar System.