The greatest homage the Romans paid to the conquerors was the triumphal Arch. In the imperial time, it was normal infact to dedicate an Arch to the victorious campaings of the emperors, thus promoting their worship.
Under the Arch were passing spectacular pageants: the victorious general, greeted by cheering crowd proceeded, on his chariot, up to the Capitol, followed by his legions bringing the spoils of the defeated enemy.
So infact, the Septimus Severus Arch was set up in 203 b.C. to celebrate his first ten years in power, and puts into evidence reliefs which tells the emperor's victories in Partia (to-day Iran and Irak) and Arabia.
Titus'Arch was erected in 81 d.c. by the emperor Domitian to celebrate the victory in Judea of his brother Titus and of his father Vespatian.

The Arch of Constantine was instead inaugurated in 315 d.c. to celebrate the victory of Constantinus over Massentius which happened three years before.
Of some of the triumphal arches there remain but few remains, often very difficult to be individualized because they were afterwards integrated in other structures, as it is the case with the Arches of Domitius, incorporated in the Acquiduct of Claudius or completly disapeared as the Arch of Augustus which spanned the Via Sacra between the temple of Caesar and the one of Castor and Pollux completly demolished in 1545, to make of them material for the building of the new basilica of St. Peter.

Other arches had quite different functions from the honorary one, as it is the case of the Arch of Janus Quadrifronte, astride of Valebro street, erected in the 3rd century d.c., as a sheltered place where merchants could carry out their own business.