The pope's own palace, built for his Piccolomini family on the south side of the piazza. Bernardo Rossellino modelled it directly on Alberti's Palazzo Rucellai in Florence — three storeys of rusticated travertine with pilasters dividing each face. The interior is more austere than you might expect: a stone courtyard, a piano nobile of large painted halls, and a private library at the back.
The real reason to come is the three-storey loggia and the hanging garden behind the palace, both opening onto a sheer drop into the Val d'Orcia. The pope could step from his bedroom onto a private balcony with the best view in Italy. The palace stayed in Piccolomini hands until 1962, when the last of the family left it to a foundation that has run it as a museum ever since.