The Piazza Grande is the most noteworthy medieval square in the city , it is currently the site of the Giostra del Saracino ( `` Joust of the Saracin '' ) . The Piazza Grande is the most noteworthy medieval square in the city , opening behind the 13th century Romanesque apse of Santa Maria della Pieve . Once the main marketplace of the city , it is currently the site of the Giostra del Saracino ( `` Joust of the Saracen '' ) .