An investigation is underway after the blaze broke out on Friday afternoon. The library will reopen to the public tomorrow.
A computer scientist from Aberystwyth is in the final five of the 'Graduate of the Year' competition.
The ITV Wales film and television archive will be donated to the National Library of Wales in Aberystwyth.
Arwel Jones, Director of Public Services at the National Library of Wales, told ITV News "our concern now is for the collection", and that it will take time for the extent of any damage to be estimated.
An Aberystwyth University student has told ITV News that water is being pumped from the top of campus, with massive hoses directed downhill towards the National Library of Wales.
Mid and West Wales Fire and Rescue Service says 11 of its crews are continuing to fight the fire at the National Library of Wales.
It is advising people "to stay away for safety."
This video - from viewer Edward Mulgrew - shows firefighters pumping water onto the library roof earlier.
The fire at the National Library of Wales was in an area referred to as 'Stack 2', where books that have been recently donated or purchased are taken.
Staff are not able to estimate what damage has been done, as they have not been able to go back inside.
Arwel Jones, Director of Public Services at the library, admitted they are "terribly worried" about the damage that may potentially have been done to the collection.
He confirmed all of the staff and readers using the library got out safely.
ITV News understands that there were people working on the roof of the National Library of Wales today, when the fire started.
Nobody is thought to have been injured.
This video - from viewer Mark Bloomfield - shows people gathering outside, as fire crews tackle the blaze on the National Library of Wales' roof.
It is thought that nobody will be allowed back inside the library until tomorrow.
Workers were all evacuated after the fire broke out.
The National Library of Wales was established in 1907.
Building began at the Aberystwyth site in 1911 and first occupied in 1916.
The building holds millions of books, maps, prints, music and film - all documenting the history of Wales.
It is home to the first book printed in Welsh, and the first Welsh translation of the Bible from 1588.
Dyfed-Powys Police has told ITV News that all of the staff at the National Library of Wales have been evacuated.
Radio Ceredigion is reporting that 300 people have been evacuated from the National Library of Wales.
The Welsh Ambulance Service says it is at the library but there are no casualties.
Mid and West Wales Fire and Rescue Service says there are not believed to be any injuries at the National Library of Wales fire.
34 firefighters are there currently, with more on the way.
The blaze is in the roof and the upper floor of an area of the building housing books.