There is a total of 15 popes in the era between 1585 to 1689. There are many which created a lot off movement in the influence in baroque art. For example, Urban VIII which was a major patron of the art and architecture during his papacy. After his death Bernini made a statue of Pope Urban VIII.
During Alexander VII papacy, he commissioned Pietro da Cortona to redesign and revisit the facilities of S. Maria della Pace.
Alexander VII also asked for Bernini to be apart of the design of the Piazza of St. Peters. He asked for Bernini to find a solution for the disharmony between the dome and facade.
Fountain of Pope Paul V at St. Peters
Sixtus V (Felice Peretti of Ancona) 1585-1590.
Urban VII (Giambattista Castagna of Rome) 15 to 27 September, 1590.
Gregory XIV (Niccolo Spondrati) 5 December 1590 to 15 October 1591.
Innocent IX (Giovanni Antonio Facchinetti) 29 October 1591 to 30 December 1591.
Clement VIII (Ippolito Aldobrandini of Fano) 1592-1605.
Leo XI Alessandro Ottaviano de'Medici of Florence) 1-27 April, 1605.
Paul V (Camillo Borghese of Rome/Siena) 1605-1621.
Gregory XV (Alessandro Ludovisi of Bologna) 1621-1623
Urban VIII (Maffeo Barberini of Florence) 1623-1644.
Innocent X (Giambattista Pamphili of Rome) 1644-1655.
Alexander VII (Fabio Chigi of Siena) 1655-1667.
Clement IX (Giulio Rospigliosi of Pistoia) 1667-1669.
Clement X (Emilio Altieri of Rome) 1670-1676.
Innocent XI (Benedetto Odescalchi of Como) 1676-1689.