Of more than 4000 isotopes of chemical elements known to us, 93% are radioactive and the majority of them are of artificial origin. Only 7% are found in larger quantities in nature as stable isotopes. A large number of these radioactive isotopes are used in research and medicine. The work with these isotopes in the Laboratory of Radiochemistry at the Paul Scherrer Institute and ETH Zurich focuses on basic scientific topics as well as on areas of applied research. For example, these isotopes help in determining the age of the universe, in the diagnosis and therapy of cancer patients, in the general understanding of the chemistry of radioelements, and in the expansion of the periodic table. In this lecture, we present an overview of the diverse research foci of our laboratory and thus dive into the fascinating world of radiochemistry.