On the Campidoglio hill, where are all the main offices of the Sindaco of the city, two buildings host the Musei Capitolini of Rome, the eldest publique museum of the world (1471) founded in obedience to Sisto IV Pope's wish.
image from wikipedia
The Cordonata Stair and the entire square were projected by Michelangelo and strongly wanted by Pope Palo III before the visit of emperor Carlo V in 1536. The sacre place, once the center of the ancient Rome, was in ashamed conditions. Michelangelo suggested to build a third Palace, Palazzo Nuovo, to enclose the space of the square.
The project was finished only after Michelangelo's death but following his original drawnings. Nowadays, Palazzo Nuovo and Palazzo dei Conservatori host the Musei Capitolini, the first public museum of the history opened in 1734.
First rooms are dedicated to the sculpture and keep some beautiful Roman bronze statues as the Spinario, depicting a young man in the act of taking off a thorn from his foot or the famous Lupa Capitolina, feeding young brothers Romolo and Remo, a real symbol of Rome. The upper floor, dedicated to the painting, hosts works by Caravaggio, Veronese, Guercino, Rubens and Tiziano.
An underground passage will bring you to Palazzo Nuovo principally dedicated to the the sculpture. Palazzo Nuovo also keeps the original Marco Aurelio's equestrian monument once placed in the center of the square.