Gibbon quotes Ammianus Marcellinus on the rioting that ensued after the death of Pope Liberius. At the time bishops were chosen by popular election, and two more or less simultaneous elections for bishop of Rome were held by different factions, one supporting Liberius' deacon Ursinus, and the other supporting Damasus. As a pagan, Ammianus is naturally uninterested in any theological differences that may have been at stake, and criticises the two candidates for ambition to enjoy the luxurious lifestyle of the bishop of Rome, in contrast to the frugal lifestyles of provincial bishops.
The prefect Praetextatus, who restored order to Rome, was said to have quipped to Damasus, "Make me bishop of Rome, and I'll become a Christian immediately." Maijastina Kahlos has a section on Praetextatus and Damasus in her book Vettius Agorius Praetextatus: A Senatorial Life in Between, which she has put online at her blog, Arduum res gestas scribere. The book, I hasten to add, is in English, although the blog is in Finnish.
The Roman Catholic church remembers Damasus more positively as the pope who urged Jerome to make a fresh Latin translation of the Bible to replace the differing versions that then existed. This was to become the Vulgate. The Catholic Encyclopedia and the 1911 Britannica both have articles on Damasus, who at some point was made a saint.