Chariot racing was one of the most popular forms of entertainment and goes back to Ramulus and by 3rd BCE there were 8 race tracks in Rome. One of the most well know was the Circus Maximus with space for 30,000 people and 12 starting gates. In 4th century there were 64 calendar days dedicated for the racing and there were ~24 races a day, with one race going around the spina 7 times, which is approx 5 quarter miles. Usually there were teams, four colored factions and they were owned by the rich businessmen. The chariot racing event was actually a good place to meet the Emperor and women... so it was a big even in Rome.

The important part about chariot racing is that it was very dangerous sport. Chariots were not designed for safety but for speed. Also, slaves were the charioteers and given the amount of races per year, there was a good chance of injury and death. As a result good racers enjoyed a little bit of fame, Diocles from 2nd CE being the prime example, he was one of the biggest winners. Got gifted the crown, golden necklace and all that good stuff.

That's as much as I recall from my undergrad class. I am less familiar with Roman utilization of chariots but from what I know, chariots were used for harassment in ancient warfare. There were two 'operators', the driver and the archer or a soldier with javalins. Given the Roman phalanx formation and the cavalry, they didn't have the need for chariots.