At the end of the 13th century the city council of Florence decided that a large cathedral was to be constructed to reflect the city’s power. More than 100 years later the construction of the Basilica di Santa Maria del Fiore was about to be completed, but there was still no dome and no one knew how to build such a complicated structure. Eventually a competition was held for the design of the dome. Filippo Brunelleschi sent in his submission and won.
On April 16, 1420, he began with the execution of his design and in 16 years he built the largest masonry dome in the world. The dome has a diameter of 45 meters and is 91 meters high.
How did Brunelleschi pull that off exactly? We do not know. He left no notes and the knowledge has been lost.
National Geographic made an interesting animation video about the construction of the dome of the Duomo of Florence.