The Museo dell'Opera del Duomo opened fairly recently; in 1986. It is located in the old chapter house of the cathedral, and in it there are a number of very interesting works, including sculptures that originally decorated the facade of the Duomo and Baptistery. 

In general, you can see that the architecture during the twelfth and thirteenth centuries was greatly influenced both Rome and Islam. 

And among the most important pieces of the museum are the impressive Arab hippogriff, half horse half tap, and "Madonna with Child" by Giovanni Pisano. 

But also from the museum's courtyard you can enjoy fantastic views of the Piazza dei Miracoli. Enjoy!