In this neighborhood of huge, austere palaces, Palazzo Spada strikes an almost frivolous note, with its upper stories covered with stuccos and statues and its pretty ornament-encrusted courtyard. While the palazzo houses an impressive collection of old-master paintings, it's most famous for its trompe-l'oeil garden gallery, a delightful example of the sort of architectural games rich Romans of the 17th century found irresistible. Even if you don't go into the gallery, step into the courtyard and look through the glass window of the library to the colonnaded corridor in the adjacent courtyard. See—or seem to see—an 8-meter-long gallery quadrupled in depth, a sort of optical telescope taking the Renaissance's art of perspective to another level, as it stretches out for a great distance with a large statue at the end. In fact the distance is an illusion: the corridor grows progressively narrower and the columns progressively smaller as they near the statue, which is just 2 feet tall.
The Baroque period is known for special effects, and this is rightly one of the most famous. It was long thought that Borromini was responsible for this ruse; it's now known that it was designed by an Augustinian priest, Giovanni Maria da Bitonto. Upstairs is a seignorial picture gallery with the paintings shown as they would have been, piled on top of each other clear to the ceiling. Outstanding works include Brueghel's Landscape with Windmills, Titian's Musician, and Andrea del Sarto's Visitation. Look for the fact-sheets that have descriptive notes about the objects in each room.