How did the Romans keep track of years before they converted to Christianity?

The Romans used to refer to years by the name of the consuls. For example the year 44 bc was the year of Julius Caesar and Mark Anthony. But because it's difficult to remember hunderds of names so they also used ab urbe condita, 'since the founding of the city'. AUC starts in 753 bc, so the year of Caesar and Anthony would be 710 AUC. And the year 2017 is 2770 AUC

Check out the calendars and timekeeping section of the FAQ.