Concha Muedra had a long career as a medieval professor and archivist.
She obtained her baccalaureate at the Instituto Cisneros in Madrid and graduated in Philosophy and Arts at the Central University of Madrid . She joined the Body of Archivists, Librarians, and Archaeologists in 1930 and was assigned to the National Historical Archive in Madrid. Since 1936, she has been Professor of Ancient and Middle World History at the Central University of Madrid.
She was purged after the civil war and went into exile in Mexico, like her sister Teresa Muedra , married to the doctor Blas Cabrera Sánchez . In Mexico, she devoted much of her efforts to cataloguing 16th and 17th century books in the National Library of Mexico .
In 1979, with democracy in place, the Spanish Ministry of Culture readmitted her to the Cuerpo Facultativo de Archiveros.
In that year, she was still living in Mexico City.