Palla Strozzi (1372–1462) neglected the family bank, but played an important part in the public life of Florence, and founded the first public library in Florence in the monastery of Santa Trinita, as well as commissioning the important Strozzi Altarpiece of the Adoration of the Magi by Gentile da Fabriano.
He was also a condottiero or leader of mercenary soldiers and after his reconciliation with the Medici and return in 1466, began the Palazzo Strozzi, which was finished by his son Filippo II.
After the murder of Alessandro in 1537, Strozzi assumed leadership of a group of republican exiles with the object of re-entering the city but having been captured and subsequently tortured he committed suicide.
He took part in the French siege of Calais (1557), and died of wounds incurred in battle at Thionville, in Lorraine, in 1558.
It is unclear whether Bernardo Strozzi (c.1581–1644), a prominent and prolific Italian Baroque painter born and active mainly in Genoa and Venice, was a part of this immediate family.
The Palazzo Strozzi in Florence belonged to the family until 1937 when it was sold to the Istituto Nazionale delle Assicurazioni (INA).