Anthony Blunt was not kind to this church: "The history of the building of S. Agnese accounts for its present unhappy state. As a background to the Fountain of the Four Rivers it is splendid enough, but as a work of architecture it is confused and full of conflicting elements. It is one of the most melancholy proofs of how seriously Borromini's difficult temperament could affect the execution of his designs."
There were too many Popes and patrons stirring up this soup, and consequently too many designers. Borromini was called in when the original architects were fired. The concave front was definitely his work. The dome and towers and pediment were not – by the time they were built Borromini had quit, in order to avoid being fired in his own turn. It was a messy story, too complicated to tell here in full, but (all the same) the surviving curves and details remain beautiful in their own right.
The fountain in front of the church became one of Bernini's most famous creations. The four heroic figures represented the four largest rivers known to 17th century Rome: the Danube, the Ganges, the Rio de la Plata, and the Nile. The figure of the Nile (immediately below) was carved holding a drape over his head. One story said that this was because the source of the Nile was unknown at that time. Another source said the reclining statue represented Bernini himself, who wanted to block out the sight of Borromini's bungled church.
The Pope supplied yet another Egyptian obelisk (found in five pieces in a Roman ruin) to make the fountain's centerpiece. I used a vintage stock photo for this overall view, since I didn't have the foresight to stand back and take a picture of the whole thing for myself.
My daughter could not see the Ganges as heroic, but merely as fat. Tastes invariably do change over time, I suppose. From about 1750 to 1950 it would have been difficult to find even one educated person who had a good word to say about any Baroque art or architecture.