In 1898, the discovery of two new elements, polonium and radium, reawakened interest in the topic of uranic rays discovered 2 years before by H. Becquerel. Radioactivity, a name coined by Marie Curie, became a major research field for decades. The contrasting personalities of Pierre Curie, already a first-rank physicist, and of the young Marie Curie-Sklodowska as they undertook their common work are described. It is shown how a well-chosen quantitative method and a systematic approach combining physics and chemistry led to the discovery within less than 1 year. The special role of radium and the determination of its atomic weight by Marie Curie followed by her long-term program for accumulating pure radium salts are emphasized. The first woman with a full professorship at a French University, Marie Curie created and managed the Radium Institute.