The name of the Church derives probably from the fact that it is constructed close to the bank of the Tiber, which in the past often used to overflow. The Church of San Salvatore in Onda and the buildings attached to it have been since 1846 the official seat of the Pallottine priests and brothers, consigned to the Society by Pope Gregory XVI. But the Church is much more ancient. The last to take care of the Church before the Pallottines were the Franciscan Conventuals who had it for about 500 years. From the Franciscan community attached to the Church San Salvatore in Onda came two Popes: Sisto IV (1471-1484) and Sisto V (1585-1590). We find a crypt under the Church which goes back probably to the 8th century.

Under the crypt, below the level of the city we find wine cellars and storerooms of Roman times.

The Generalate House was the host for some weeks to the young Carol Wojtila in 1946 during his stay in Rome for study.