As my friend and I were walking back to our hotel from the Spanish Steps, we happened on to this place and didn't know what it was. I had to look it up!
The official residence of the presidents of the Italian Republic since 1947.
Set on the Quirinal Hill, the highest of the seven hills of Rome, the building - which extends over an area of 110,500 square meters, making it the 6th largest palace in the world (the White House is 20 times smaller) - has housed 30 Popes, four Kings of Italy and 11 presidents of the Italian Republic.

The palace was originally built as a papal summer residence in 1583 by Pope Gregory XIII, who wanted a location removed from the humidity and smell of the river Tiber and the unhealthy conditions of the Lateran Palace. The site had been in use since Roman times.
After Rome became the capital of the new Kingdom of Italy in 1871, the palace became the official royal residence of the Kings of Italy. Following the abolition of the monarchy in 1946, the Palace became the official residence and workplace for the Presidents of the Italian Republic.