From 1450 to 1600. Renaissance is literally the rebirth of the classical styles of ancient Rome and Greece in all the arts: literature, music, architecture, sculpture and painting. The advent of the Renaissance meant mankind was emerging from the Middle Ages.
The Papacy had returned to Rome after three quarters of a century in Avignon; artists and patrons were in a celebratory mood. In architecture, Romanesque with its heavy rounded shapes, as well as Gothic with its pointed windows and doors had lost their charm. Suddenly, the ancient Roman edifices, that had been pillaged or neglected for a millennium, seemed perfect prototypes for the buildings of this exuberant age.
Many historians say this movement started in Florence with the rediscovery of ancient Greek and Latin poetry, and soon spread to encompass the visual arts. Pope Martin V (1417-31) is credited with launching the Renaissance in Rome with his vast program of reconstructing Rome including its ancient buildings as well as restoring the early churches.
This movement culminated in the High Renaissance (1500 to 1520) when the three giants, Leonardo, Michelangelo and Raphael were spreading their enlightenment in Rome.
From 1530-1600. Mannerism is the name given by art critics to the last phase of the Renaissance which started the transition to the Baroque, roughly 1530-1600.
Michelangelo, in the second half of his life, was principally responsible for spawning this style, typified by the distorted figures in some sculptures and portraits, with long thin necks and heads. The poses are "mannered" in the sense that they are exaggeratedly dramatic rather than natural.
This esoteric movement led to the irrational treatment of space and a sense of psychological unease, such as we see in "The Last Judgment" in the Sistine Chapel and even some of Michelangelo's architecture such as the Laurentian Library in Florence.
From 1600 to 1750. Baroque art, and especially architecture, emphasizes decoration and movement, using classical elements but in an exaggerated manner meant to inspire religious spirituality.
It reached its apogee right here in Rome with the palaces, fountains, and sculptural tableaux of Bernini, as well as his churches, and those of the apprentice who surpassed him in architecture, Borromini.
This style, too, erupted at a period of enthusiasm and optimism, the Counter Reformation, when the Catholic Church had emerged from the ugly skirmishes with Protestant antagonists and the Popes were eagerly spending the Holy See's riches to enhance their families and their fame.
Grim and cheerless unadorned buildings were so repugnant to the Italian temperament that this new, dynamic style, which at first was greeted with derision, was then accepted enthusiastically by the Romans.