She was the director of the Spanish National Cancer Research Centre (Centro Nacional de Investigaciones Oncológicas, CNIO) from June 22, 2011 to January 29, 2025.

She obtained her PhD in 1993 for her research at the Centro de Biología Molecular Severo Ochoa (UAM-CSIC), under the supervision of Margarita Salas.

That same year, Blasco joined the Cold Spring Harbor Laboratory in New York (USA) as a Postdoctoral Fellow under the leadership of Carol W. Greider (who was to win a Nobel Prize in 2009).

She joined the Centro Nacional de Investigaciones Oncológicas (CNIO) in 2003 as Director of the Molecular Oncology Programme and Leader of the Telomeres and Telomerase Group.

In 2005, she was also assigned as Vice-Director of Basic Research, and, in 2011, she was appointed as CNIO Director, replacing Mariano Barbacid.