Short answers, pulled from the story.
Baroque architecture was introduced by the Catholic Church, particularly the Jesuits, as a response to the Protestant Reformation. It was designed to inspire astonishment, reverence, and awe in worshippers, making churches and religious spaces overwhelmingly dramatic and theatrical.
The High Baroque peaked between 1625 and 1675. This period produced major works in Rome by Gian Lorenzo Bernini, Francesco Borromini, and Pietro da Cortona, and saw the style spread to France, Venice, and beyond.
Pope Urban VIII, who held the papacy from 1623 to 1644, was the most influential patron of the Baroque style. After Carlo Maderno died in 1629, Urban appointed Gian Lorenzo Bernini as chief Papal architect.
Quadratura is the technique of combining trompe-l'oeil painting with sculpture on ceilings and domes to create the illusion that the viewer is looking directly through the ceiling into the heavens. It was one of the most distinctive visual effects of the Baroque style.
The Churrigueresque style is a highly ornate variant of Spanish Baroque architecture named after the architect Jose Benito de Churriguera and his brothers. It originated in Madrid and Salamanca and is characterized by buildings nearly overwhelmed by gilded wood, gigantic twisting columns, and sculpted vegetation. The style was also exported to Latin America.
Ottoman Baroque emerged in full expression during the 1740s. The Nuruosmaniye Mosque complex, begun by Mahmud I in October 1748 and completed by Osman III in December 1755, is considered its most important monument and marked the integration of European architectural culture into Ottoman building practice.