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.
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Swansea City failed to capitalise on last weekend's dramatic win over Crystal Palace, as they fell to a heavy 5-0 defeat away at Tottenham.
Post Office workers and managers have held a third strike in a long-running dispute over job losses and pensions.
After a cloudy start it will be a dry day today. The cloud will break up this afternoon, with some bright or sunny spells developing