The first bridge in this location was built in 1252; however, the bridge as it appears today is based on the bridge built by Bartolomeo Ammannati from 1567-70. Like all the other bridges in Florence except the Ponte Vecchio, Ponte Santa Trìnita was destroyed by German forces in 1944. Some of the stones from the original bridge were recovered from the Arno, and an exact replica was built using these stones along with stones specially quarried from the Boboli gardens.
In addition to the graceful, flattened arches that span the river (which some attribute to Michelangelo), the bridge is also decorated with statues of the Four Seasons, which appear at each corner of the bridge. Fall, holding aloft a bunch of grapes, and a denuded Winter greet you as you cross the bridge from the Oltrarno, while Spring and Summer watch as the bridge deposits you onto Via Tornabuoni. These statues (or most of the parts) were recovered from the Arno after the demolition of the bridge in 1944 at various times and were eventually returned to their original places.
The NY Times article on the reopening of the rebuilt bridge in 1958.