The set of buildings called the Compendio or Complesso di San Silvestro is located in an irregularly-shaped, tree-lined square near the Arno River. It was probably founded in 1118, when the Pisan Archbishop Pietro Moriconi gave the church and monastery connected to it to the Benedictine Monks of Montecassino , who remained there until 1270.
The Romanesque church, which can just barely be made out in the apse and bell tower, was decorated with many ceramic basins. In 1331 the buildings were given to the nuns of San Domenico from the nearby convent of Santa Croce in Fossabanda; they restored the church for the first time. The changes carried out in the 17th and 18th centuries were more substantial: In 1609 the church was divided into two parts in order to create a choir or internal room for the nuns; during the 18th century the façade was completely redone, the architrave (now kept at the Museo Nazionale di San Matteo) with the histories of Constantine and Silvestro removed, and statues added. The church was deconsecrated and used as a workshop for the restoration of art.
The 14th-century convent connected to the church has been used in various ways over the centuries. In 1782 the Grand Duke of Tuscany, Leopoldo, transformed the monastery into a conservatory for the daughters of nobles; at the beginning of the 19th century it became the property of the Order of the Salesians. Also in the 19th century, it was the seat of the Scuola Normale, subsequently becoming a reformatory for minors and then a student residence.
The building is currently undergoing important structural restoration by the Scuola Normale Superiore, to host the new science centre, including the NEST research institute, and the SMART laboratory.