The Strozzi family grew rich through commerce and took an active part in the government of Florence after the 13th century. In the fifteenth century, the Strozzi strongly opposed the Medici rule of Florence and were exiled when Cosimo de' Medici seized power in 1434.

At an early date the family divided into several branches. Palla Strozzi, c.1373–1462, a politician and ardent humanist, furthered Greek studies in Florence and Padua. Filippo Strozzi, 1428–91, son of Matteo Strozzi, gained wealth and influence in Naples, and returned to Florence in 1466.

His son Filippo Strozzi, 1489–1538, married a granddaughter of Lorenzo de’ Medici; he was first friendly to the Medici, then became a staunch opponent. He led Florentine exiles against Cosimo I de’ Medici, was captured, and died in prison.

His son Leone Strozzi, 1515–54, first entered the Order of Malta and later became an admiral in the French service. He distinguished himself in wars against Spain and England.

Another son of Filippo, Piero Strozzi, d. 1558, a violent enemy of the Medici, fought for the French in the Italian Wars and was made a marshal of France. He took part in the French siege of Calais (1557).

Filippo Strozzi, 1541–82, was also in the French service. He was captured and killed by the Spanish in a naval battle off the Azores.