Today most of the ancient Dominican convent, including the Great Cloister, is occupied by the Carabinieri Officer's School, to whom one has to apply for permission to visit it. This part of the Convent also contains the apartment that the Florentine Republic commissioned Lorenzo Ghiberti to build in the fifteenth century to accomodate the Popes and other illustrious visitors to the city, and known as the "Florentine Lateran" for this reason.

It also hosted the various sittings of the Florence Council in 1439 and the Patriarch of Constantinople died and was buried here. Little remains of this apartment today, only the tiny Chapel of the Popes, painted in 1515 by Ridolfo del Ghirlandaio and the young Pontormo on the occasion of the visit to Florence of Pope Leo X, perhaps better known as Giovanni dé Medici, the son of the Magnificent.