The church, in its "nuova" form, which is seen today, was built to provide a base for the work of St. Philip Neri and his Congregation of the Oratory. The Chiesa Nuova complex includes the church, the oratory (with Borromini's justly famous façade), the Vallicelliana library (including one of the world's best collections of early music, especially "Oratorios"), and the convent of the Oratorian Congregation.
By the time Pope Gregory XIII began the 1575 rebuilding, the earlier buildings had seriously deteriorated. Gregory XIII gave the tumbled-down pile to Philip Neri and his new counter-reformation religious order. The overall plan of the new complex was by Matteo di Città di Castello and by Martino Longhi the Elder, who also created the dome together with Giacomo Della Porta. The Chiesa Nuova was finally inaugurated in 1577. The new building reflected the inclination of Philip Neri and, in fact, according to his wishes, the nave was painted stark white (gold stucco and ornamentation added in the 18th century), and all the altars of the chapels were dedicated to the Virgin Mary. Philip also successfully lobbied the Pope to house the ancient image of Santa Maria in Vallicella in the new church, and the painting was moved to the church even before the complex was completed. It is still there today, but it is behind Peter Paul Rubens' Madonna above the main altar. It is only occasionally exposed for public view.
The facade was finished after Philip Neri's death in 1605, and construction of the other areas of the complex and the final decoration of the church continued throughout the whole of the following century. The Chiesa Nuova is famous for the large number of paintings which now decorate its interior -- the work of Baroque masters such as Caravaggio, Rubens, Federico Fiori di Urbino (il Baroccio), and, above all, Pietro da Cortona. Architect and painter, Pietro di Cortona added the spectacular lantern in the dome, which replaced one of an earlier and far simpler design. The Rubens Madonna, mentioned above, was painted early in Rubens' career and it is flanked by two more of his paintings from the same period. Alessandro Algardi's larger-than-life statue of Philip Neri and his bronze bust of Gregory are in the sacristy, and Guido Reni's portrait of Philip is in Philip's restored apartment (open only on the feast of St. Philip, May 26.)
There are several good Internet sites describing Santa Maria in Vallicella, but none of them can compete with the real thing, which you can visit mornings and late afternoons Monday through Saturday. The church is open for masses only on Sunday mornings.
The best of the Internet sites is the "official" site of the Oratorians at http://www.dslabs.it/chiesanuova/en/index.html where you can find links to the life of Philip Neri, the history of the church and adjoining buildings (with a floorplan), and a virtual tour of the church with pictures of the highlights.
An informative article on the Church by June Hager, a former US Embassy employee who more recently has written for "Inside the Vatican" magazine, is at http://www.initaly.com/regions/latium/church/cnuova.htm.
Old drawings and modern photos of the Church and Oratory, with informative captions are at http://www.geocities.com/Paris/LeftBank/7798/Vasi/Vasi137.html.
Neri's bio from the Catholic Encyclopedia is at http://www.newadvent.org/cathen/12018b.htm, and the Oratory story is at http://www.newadvent.org/cathen/11272a.htm.
Overhead views of the Church, Oratory, and surrounding areas are at http://cidc.library.cornell.edu/romephotos/index/small/88s.html and http://cidc.library.cornell.edu/romephotos/index/small/89s.html
P.S.: The "oratorio" musical format, which is acknowledged to be the precursor of the Opera, originated in the Oratorians' services. This dramatized form of usually sacred music is similar to opera, but without action and scenery. Giovanni Pierluigi da Palestrina (1525-94) originated the form in compositions that had their first performances at the Philipine Oratory adjacent to the church. The genre was subsequently developed in masterpieces by Heinrich Schutz, Johann Sebastian Bach, Georg Friedrich Handel, and Franz Josef Haydn.