In a hazy, dreamy, sun-baked Rome in an August afternoon the timid, precise law student Roberto (Trintignant) is asked by a 40-ish man named Bruno (Gassman) passing under his window at the wheel of a convertible Lancia Aurelia for a trivial favor: a phone call.
The young man tells Bruno to come up and make the call himself; after he fails to contact his friends (he's a full hour late for the meeting they had) Bruno insists to repay Roberto's courtesy by offering him a drink. Being tired of studying for the day the young man accepts.
Thus begins a cruise along the Via Aurelia (the Roman road which also gives the name to Bruno's car) where Roberto is unwilling or unable to part from his casual acquaintance despite having nothing in common with him. Bruno is loud, direct, a bit coarse and a braggart to boot but also charming and likable, Roberto, being his complete opposite, feels drawn to his impulsive and devil-may-care attitude.
In two days of high and lows across the coasts of Lazio and Tuscany the two men manage to learn something from each other (Roberto discovers his childhood hasn't been as golden as he always maintained, and finds out about Bruno's failed marriage and young daughter realizing he's not half as carefree as he pretends).
Their friendship and male bonding is cut short when, urged by Roberto, Bruno attempts a risky maneuver resulting in an accident. The younger man falls with the car along a rocky cliff, leaving a bloodied and shocked Bruno on the curve's edge, realizing that in the time they spent together he had not even asked him his surname.
The movie is considered one of the best Commedie all'Italiana ever and a poignant portrait of Italy in the early 1960s when the "economic miracle" (dubbed the "boom" - with the actual English word - by the local media) was starting to transform the country from a traditionally family-centered society into an individualistic, consumeristic and shallower one.