Short answers, pulled from the story.
Pope Sixtus IV established the museum in 1471 by placing a collection of ancient bronzes on the Capitoline Hill for the people of Rome. This act included works such as the Capitoline Wolf and the Boy with Thorn which had been kept in the Lateran Palace until that moment.
Michelangelo Buonarroti designed the square renovation project commissioned by Paul III during the 16th century. He died during the works in 1564 leaving his design incomplete before Guido Guidetti and Giacomo Della Porta completed it in 1568 following Michelangelo's designs almost faithfully.
Pope Clement XII opened the museum to the public in 1734 making it one of the earliest museums accessible to all citizens. In 1733 under Pope Clement XII the museum purchased the collection of Cardinal Alessandro Albani including pieces like the Satyrs of the Valley and the Juno Cesi.
The Capitoline Venus was returned to the Capitoline Museum in 1816 after being taken to Paris in 1797 following the Treaty of Tolentino. Antonio Canova remedied the Napoleonic spoliations through obstinacy after the fall of Napoleon and reported back in 1815 with works like the Boy with Thorn and the Dying Gaul.
The Palazzo dei Conservatori is remembered as the place where the Treaties of Rome were signed in 1957 establishing the European Economic Community. The Hall of the Horatii and Curiatii often hosts important ceremonies including this historic signing involving Belgium France West Germany Italy Luxembourg and the Netherlands.
A branch opened in 1997 in the former Centrale Montemartini thermoelectric factory located in the Ostiense district. A full-scale reconstruction of the Colossus of Constantine was installed in the gardens of Villa Caffarelli in 2023 while the museum continues to attract visitors from around the world.