The square has been known by this name since around 1150 when the Crusaders built the monastery with the adjacent hospital, and the church dedicated to Santa Maria Assunta. The church was burned down and then rebuilt a first time in the early 13th century, and then again in the early 1500s. In the 15th century, all of the convent buildings were confiscated as a result of the order’s scandalous behaviour, and the monastery was given to Cardinal Bessarione. The complex was expanded in 1514, and again in the 18th century. In the 17th century, a papal decree ordered the permanent elimination of the Order of the Crusades, and all of its wealth was appropriated by La Serenissima to finance the War of Candia. Starting in the early 1600s, the complex was transferred to the Jesuits, the church was torn down in 1715, then rebuilt according to the religious criteria of the times, remaining a subsidiary of the Santi Apostoli parish, while the convent was used first as a public school, then as barracks for the military police (Carabinieri). 

It still stands in the square Ospedale dei Crociferi in its original form

We also see the building used as by the furriers (varoteri) as their association seat until the early 18th century, when it was transferred to Campo Santa Margherita