The Pinacoteca Vaticana, or Vatican Art Gallery, was created in 1932 and is in a building that was specially commissioned by Pope Pius XI. As you walk to it, and especially when the weather is nice, take advantage of the beautiful Vatican Gardens for a pleasant, cool break.
Paintings from the Vatican Palaces await, with masterpieces ranging from the 1200s to the 1700s: the first one you'll see is the Triptych painted on both sides by Giotto around 1320. This painting was once on the altar of Saint Peter's Basilica. In the middle panel on the front, you can see St. Peter sitting in a chair: to the left of his feet you can see the cardinal who commissioned the work, holding up a model of the triptych itself. Make sure to look at the back as well, where you'll see the scenes of the Martyrdom of Saints Peter and Paul, one crucified upside down and the other decapitated.
I'd like to point out a great fresco by Melozzo da Forlì in the section dedicated to the 1400s. It comes from the old Vatican Library and is titled Sixtus IV Appointing Platina as Prefect of the Vatican Library. The work is set in front of majestic Renaissance architecture with a blue and gold paneled ceiling. It depicts the ceremony in which Sixtus IV, in the presence of other figures of the papal court, entrusts the direction of the library of the Holy See to the humanist Bartolomeo Platina, who is kneeling in the middle. The architectural representation in the scene perfectly follows Leon Battista Alberti's lessons, who had theorized the laws on perspective, while the firm but serene composition probably reminds you of Piero della Francesca.
The fascinating St. Jerome in the Wilderness by Leonardo dates back to the second half of the 1400s, and is one of the Pinacoteca's greatest symbols. This work is a middle ground between a painting and a drawing. The figure of the saint being whipped for penance is defined with an accuracy that brings out both the physical and spiritual tension. In the lower left, you can see the outline of the lion that always accompanies the saint in his depictions.
FUN FACT: one day a richly dressed man entered Giotto's workshop and presented himself as having been sent by Pope Benedict XI, who was looking for a painter to assign an important job to. He wanted to take away a canvas, but Giotto instead painted a large "O" by hand on a blank sheet of paper, and told him to take it to the pontiff. It was such a perfect circle that it looked like it had been drawn with a compass. The pope was so impressed that he chose Giotto among many other painters, and called him to Rome.